A man, past his prime but not yet old, with worn clothes and a ragged haircut, approaches.  Despite his appearance he has a bit of energy to his step, as if he had heard some piece of good news or made some happy decision recently.

Even with the money he appropriated stole (he’ll be honest with himself about that much) he can’t really afford to buy anything that isn’t strictly practical.  But he would like advice about traveling through the region… and maybe someone to watch his back along the way.

“That’s an interesting cart you have.  Have you traveled far with it?”

He fumbles around with (one of) his coin purses, to make it clear he has money and is a potential customer.

"Yeah, quite the nice construction isn't it? I go all along the southern coasts. So long as you can still do commerce freely there, anyway. Foggy Swamp, the edge of the desert, and past the barrier mountains..."

"Do you have any wares you would recommend to someone planning to travel to the great desert, and perhaps around it's edge?  …I'm looking to be far away from anywhere worth fighting over if the Fire Nation starts a new offensive or if the Earth Nation pushes back."

"...There aren't a lot of places that are definitely safe, these days. Ba Sing Se is the closest you'll get, and it's a long, long way away from here. Are you used to rough living?"

That problem with Ba Sing Se is that it might be sophisticated and proactive enough to identify and eliminate former Fire Nation soldiers.

“I haven’t roughed it for extended periods of time, but I think I can learn to cope.  And I was worried the Fire Nation might make another push towards capturing Ba Sing Se.  Of course they will fail but it wouldn’t be safe to approach the city if it’s under siege.”

So that's a 'no'.

"One hears rumors that there are ways. Of course, being so far from Ba Sing Se, I wouldn't know if those are just rumors or not. Gao Ling is the largest stop on my route south other than Omashu, which lies behind me, and it is still safe... For now. I wouldn't rate their chances high if the Fire Nation decides to go there in force, but they have a lot of other places to deal with now don't they? And Gao Ling is not nearly as symbolically important as Ba Sing Se, or even Omashu."

The Fire Nation army often has cripplingly logistical issues from graft and incompetence so it’s not exactly easy living!  He isn’t going to explain that though!

“Gao Ling sounds like a reasonable place to go… are you on your way there?”

He lets the coins in his purse clink a bit.

“My biggest worry isn’t actually about the Fire Nation… have you heard the rumors about what happened to their Northern Fleet?”

"You don't have to show off your money... Oh? Something new to report? News travels at the speed of messenger hawk for some but foot for the rest of us."

He was trying to be subtle about his money, but he really isn’t calibrated to life outside the army!

“So you know how the Fire Nation propaganda and wanted posters kind of alternate between portraying the Avatar as an effeminate feckless child and as having a bunch of dangerous esoteric bending techniques?  It’s looks like the second description is the accurate one.  The Northern Fire Nation fleet had recently massed for a single crushing blow on the Northern Water Tribe, and it looked like they would be successful, but the Avatar wiped out their entire fleet in less than a single night.”

He smiles, a bit manically.

“So the Fire Nation is probably all fucked.  Best case scenario for them is Kyoshi Island a few times over.  Worst case scenario… their islands have a lot of volcanoes I hear.  So the rest of the world is saved, we just need to stay away from the Fire Nation and any fault lines or dormant volcanoes or areas susceptible to rock slides or other such areas that might get set off by distant cataclysms until it’s all settled.”

"...Well."

Deep breath.

"Bearing in mind that this is one rumor, that would seem to indicate the Fire Nation going down sooner or later, wouldn't it? A lot of people could get burned in the meanwhile, though. Spirits of ancient days, how must you feel about the stupidity of human design...?"

“I’m pretty confident in my source…”

Namely himself, snooping through messages he didn’t have the authority to read but his commanding officer was too sloppy to keep properly secure.

“It would be just like the Fire Nation to make one last suicidal push out of pride or idiotic refusal to admit defeat.”

"Quite. Well, one can hope that Gao Lin or... I'm not sure where fault lines are. Away from mountains and from the coast and... It sounds like the great desert might be the safest place, inhospitable as it is..."

“Yes, you can see my reasoning for the desert.”  

Well that, and the fact that it’s far enough from the war that the common people won’t want to kill a fire bender on sight.

“I don’t need much, just enough civilization that I can spend my money and work a modest trade without being robbed.”

"I don't know much about living in a desert. I've skirted the edges and even with clever contraptions there's no water to be found. The deeper oasis towns, well, presumably people live there and do trades."

“Do you know of any villages on the outskirts that have trade with the deeper oasis towns?”

"Misty Palms oasis. Right at the very edge of the Si Wong Desert, literally a few hundred feet from where the green ends. I pass by there on my way south because I get decent custom there, it's a bit of a desperate market. I try to leave the same day I arrive. A bit of a harsh place. And there's a not insignificant chance of danger. There are people watching the obvious last call before driving into the desert, you see. For easy marks."

“Ah, yes, that sort of barbarism is what I was afraid of.  Maybe I should go to Gao Lin then, and just hope it isn’t subject to a last desperate suicidal attack by the Fire Nation.”

"They are pretty civilized and traditional in Gao Lin. I'd rate your chances of a peaceful time higher there."

“Will your current route take you to Gao Lin?  Would you mind a traveling companion along the way?”

He resists the urge to fidget with his purse.  He’ll hold off on offering money, why pay if he can get help for free?

"...I generally move alone. Or with reasonably close acquaintances whom I have known for some time. I can sell you travelling supplies, though."

“Well I certainly need some of those!  How strongly committed are you to traveling alone… like, if you had to put a monetary value on it?”

And if money doesn’t work, he has one more bribe to try, but it will reveal a lot more about himself than he wants to.

"It's not about the money, it's about risk, and trust. I'm sure you would understand that, seeking a safe place yourself?"

He stands and starts digging through cabinets built into the little open side of the wagon.

"Waterskins. Firestarter- Just flint and steel in a little doohickey. Scroll on basic fieldcraft. I can whip up a tent in a couple of hours. Warm blanket. Oil lantern, plus oil. A good backpack... A good, reliable work knife if you don't already have one... Camp cauldron, which is just a pot with hooks to hang off five sticks set up as a stand... Oh, rope and cords. Chalum powder, to relieve fevers, and lemon oil you can rub on your skin to drive bugs away."

It will ruin the carefully cultivated refuge image he has going, but it does all sound useful, especially as he passes through less populated areas where there is no one to fool in the first place.

He starts counting out coins and preparing to haggle.  He knows what things nominally cost in the Fire Nation’s army’s ledgers, and how much you can get for slightly burned stuff recently looted, but he isn’t quite sure of typical normal prices.

He might as well make his play now, it might at least give him some leverage in haggling.

“If money isn’t enough to tempt you to take a risk… how about knowledge?  The Fire Nation has experimented extensively with ratios of fuel to water to boiler sizes and a source of mine obtained some of their research.  I don’t have the writings on me, but I can reproduce many of the more key finding from memory, like some of the tables comparing designs and ratios.  I think you would be quite interested… that stove part isn’t just for heating food now is it?”

Glance around... Nope, everyone's just going about their day still. It's well after lunch, and the trickle of customers has been absent for a while.

"A source. Right... I've found it to be a painful struggle to adapt certain methods and techniques being developed by the Fire Nation. And found limited success, but still constant problems, not to mention the hostility and suspicion it tends to provoke. But I believe a tool is a tool - and though I have been scolded in the past for certain directions of inventions... I rather don't like being told what not to do, you see? And thus, I go through a lot of metal and coal."

Wey Fu does his own glance around.  He smiles nervously.

"What if you needed a lot less coal?  And you didn't need any coal for your cart?  I could help with that... let's just say I don't need that flint and steel."

He had meant to probe a bit more before this reveal, but this peddler is already getting suspicious.  And it sounds like the peddler has a reason to want to avoid suspicion himself, so Wey Fu has at least some leverage against simply being turned in.

"Ah, but that we all could escape the circumstances of our birth. Why don't you come inside my humble home for a bit? At the back. I'll put on tea."

That actually worked?

"My name is Wey Fu, by the way, sorry for the lack of introduction."

He uses his real name, it isn't particularly unlikely as an Earth Kingdom name or common as a Fire Nation name.

He walks around to the back.

"I'm Shao Nin. Come on, then..."

The interior is cramped. An all in one living area with hardly any room to move between all the cunning boxes and cabinets. The table folds out of the wall, as does the bed. In fact, what was previously a display of items has become a shelf and desk on the interior as he folds things away. The boiler at the back is a weirdly bulbous thing, almost egg-shaped with a wide, flat structure on top and a large flywheel with linkages leading elsewhere right against the back wall, half covered by it. 

He draws near boiling water from a valve on the side, to make tea with.

"I have some sympathy for those who are born into a family that does not suit them." His tone is dry in a way that indicates he is part of this classification.

"Neither of us wants a mess, do we? Destruction, screaming, accusations, all that. Too troublesome to bother with."

“Yes.  I think both of us have clear incentives to keep each other’s situations private?”

Maybe he misread the situation  Shao Nin wasn’t accepting his offer, but rather wanted some privacy before refusing it?

“You can be assured of my discretion whatever your decision about my offer.”

Even with the seriousness of the situation, the boiler distracts him as he studies it and compares the design to Fire Nation designs he has studied.

It's clearly coming from almost an entirely different direction. The pancake shape is probably the working cylinder given the shaft and gearing connected to the flywheel, but it's far too wide and flat according to what Wey Fu knows. The device is not in motion right now.

He pours tea. Ordinary green, the kind that can be bought anywhere.

"I'm a misanthrope. I prefer my solitude, dealing with people is stressful, trust is a rare and precious thing that takes many moons to build and five seconds to destroy. I would prefer any deal we work out being clearly spelled out, even if there is no earthly authority either of us would be willing to go to in case of a dispute. You are implying that you are a firebender, correct?"

He wonders if the design is simply bad… or if it operates off subtly different principles than typical Fire Nation designs?  He’s really curious, but he needs to focus for now.

“That’s correct.  I lack the anger and hatred for powerful offensive Fire Bending-”

(Ever since witnessing his first massacre.)

“But give me metal that needs mending, a steam powered device that needs heat, or a furnace that needs stoking to just the right temperature and I can maintain a steady constant heat with the precision to rival a master.”

"A far better use of it in my opinion. Well, you want to get to Gao Lin and settle in there nice and quietly, I suppose. You'll need a story, and introductions... Do you know an ordinary trade? Carpentry, scribing, shoe-making or something like that? Smithing would be too much a risk."

"Hmm, smithing is probably my best non-bending trade, but yes too much of a risk of a subtle bit of automatic bending.  I'm able to handle bookkeeping and transcribing messages well enough, at least according to Fire Nation army standards.  I know the sorts of things a decent seaman knows... for steam-powered ships, not sailing."

He also has quite a bit more money they he showed to help get himself established, with two other purses concealed on his person (with soft material stuffed between the coins so they won't jingle), but he'll hold of on revealing that.

"Not many will trust you with their accounts when you're a fresh face. Transcribing messages and copying scrolls, might work. If you've a steady hand and produce good results, parchment and ink aren't cheap. Can you do arithmetic...? There's always the- No, you wouldn't want to get involved. Forget I said anything. So, to Gao Lin travelling together, introductions, and advice on a story to rely on, in exchange for... Information on engines and boilers, and some - assistance with fuel - and some coin. Does that broadly sound fair?"

He thought he was doing at least okay on a story... okay yes he needs help there.  And introductions could be invaluable for securing skilled work.  If the Avatar takes him time punishing the Fire Nation he could be in hiding for quite a few years.

"Yes, that sounds broadly fair.  Your boiler design is a bit different than what I'm familiar with... it shouldn't be a problem as long as your different design doesn't require a substantially higher maximum temperature than a comparable fire nation design.  And conversely, if you've figured out something with a lower heat requirement, I could do even better than I was expecting on saving you fuel.  ...It would be best if I could check how my fire bending interacts with your boiler and engine before we finalize the exact expectations on fuel I can save you."

He means this quite seriously (if he can replace almost all of the need for fuel, maybe he can get a better deal on the payment in coin)... but also he is really interested in seeing an entirely new boiler design, even if its unusual appearance turns out to be from bad design as opposed to something unprecedented or at least novel.

"Well, I have no idea how the Fire Nation does it but fuel is expensive so I tried quite hard to make it efficient. We can take a look when we finish this tea. No sense wasting it already poured."

Sip.

Is it poisoned?  If this man hates the Fire Nation and wants to kill him quietly so his own secrets aren't exposed, poison would be an option.  On the other hand, he will be trusting this man for a rather long journey with lots of opportunity for betrayal, so he'll have to trust him at some point.

Sip.

He smiles appreciatively.

"So... Story. You can not want to talk about it, that's understandable, and certainly don't volunteer information, but you'll want something to tell people. Ahem."

He affects a high-pitched fake voice. "Oh, you're fleeing the Fire Nation. Those bastards are ruining everything. Was your village destroyed? Are you looking for family? Maybe you can reunite with them here where it's safe! Where did you say you were from, exactly?"

"...And best not claim familiarity with a place you're not familiar with. Ahem."

"You know my great uncle on my father's side used to live in Omashu, you know, around the lower basalt district right near that one vegetable seller that always had eggplants out front, right under one of the delivery chutes- What do you mean 'what delivery chutes'? Are you REALLY from Omashu?"

More tea. Screwing around with voices makes him thirsty.

"Do you think being from a the village under long-term occupation by the Fire Nation would be too suspicious?  There are a number of them I could describe in elaborate detail, and I could likewise describe a plausible escalation in Fire Nation brutality and oppression that motivated me to leave in a hurry."

"Plausible, and preferably it was a real one that was really destroyed or at least gutted. You don't want to go into elaborate detail at the drop of a hat though. Being too rehearsed about it could be bad, too, people don't give their life story out to everyone. Remember your character- They grew up there, and the way that village lived was just normal, and the brutality was horrifying. And anything that makes people confused, differences in turns of phrase or holidays or which spirits to propitiate or what have you, was probably... Fire Nation propaganda eroding your heritage."

"Yes, I have just the place in mind..."

He doesn't want Shao Nin dwelling on exactly why he can remember brutalized and displaced Earth Kingdom villages so clearly... he should change the subject.

"So you said you could make a few introductions in Gao Lin?"

"Oh, sure. Shopkeepers, artisans, the head servants of a couple of local lesser nobles, my usual customers. I'm not gonna promise them the world, but I'll corroborate a tragic story and say you've got a head for writing and numbers if I observe these traits during our trip."

"I can definitely demonstrate those traits.  Hmm... related question, the mathematics with ratios and proportions the Fire Nation uses in it's steam engine designs and similar engineering.  Do I need to avoid showing that mathematical knowledge because it would be too obscure or foreign and thus suspicious, or does the Earth Kingdom have that sort of math also?  I don't know if, for example architects would also use it.  We should probably thoroughly go through mathematical and scientific nomenclature at some point if we don't cover it while I'm explaining my information about steam engines."

Hopefully he didn't just insult the man by implying the Earth Kingdom is backwards or whatever, but he needs to avoid revealing himself and forgetting himself while excitedly explaining some finer point of mathematics is the exact sort of mistake he is prone to making.

"Hard to tell, it's not like the Earth Kingdom doesn't produce any mathematicians or engineers? Maybe brush up on static force analysis and architecture. There's math that goes into large buildings, aqueducts, and the like, and that's a very Earth Kingdom-respectable sort of math."

It sounds like the Earth Kingdom has developed some branches of mathematics much further than the Fire Nation!  He had thought he had learned how to see through the Fire Nation's propaganda, but it seems like he still has a lot to unlearn and relearn.  An out-of-place deficit in knowledge might get him killed, but the excitement about the chance to learn some new math is outweighing his fear, at least for the moment.

"I would very much like to learn more about that sort of math."

He isn't bothering to conceal his excitement, this man is clearly an intellectual, at least in an eccentric loner sort of way, so hopefully he will sympathize with Fu's excitement, or at least not actively look down on him.

"It is quite interesting. The big one is various methods of approximating the total force acting on different parts of a large structure, derived through a method called the 'integral'. The usual example is a dam holding back a great mass of water..."

He can explain some of the not-quite-calculus that has been popular in higher end Earth Kingdom academic circles as they finish the tea. It suffers a bit from lack of writing material to demonstrate on, though.

This partnership is already paying off!

He follows as best he can.  He enthusiastically asks questions.  His questions aren't exactly the most insightful, but he does seem to be getting the concepts.  Some of his questions are a bit off-base, perhaps from a lack of writing material to put the concepts to paper, or perhaps because he is already looking for ways to extend the methods to more dynamic engineering problems, such as a steam engine in motion or a boiler holding steam.

Now that the tea is gone they can get out his chalk and slate and do the math more properly. And look at his engine.

"So, the key observation I have made is that hot air expands, and cold air retracts. This wheel here is big and heavy enough to keep everything moving along. It turns, The plate inside this box here moves up, and the air inside the exchanger moves to the side closest to the boiler. It gets hot, and expands. That makes this - piston over here - push out, which adds a little bit more energy to the wheel. Then, the wheel keeps turning. The plate moves down, and pushes most of the air in here to the cool side. It contracts. This piston is then driven to retract by the pressure, and again adds a bit of energy to the wheel. And then it moves up again, air to the hot side, expand... The big problem is making the system overcome friction without losing too much force, and that it's not all that powerful. Though it does seem to be a bit more efficient, heat-wise, than boiling steam from what I've been able to guess?"

"Air instead of steam... remarkable!  And it would obviously be less powerful yes... but you think it is more efficient?  Losing power for efficiency does seem like the sort of thing tradeoff Fire Nation might have easily overlooked considering properly."

He's excited.  He starts talking fast in his excitement.

"I can gauge how much heat I'm putting out almost exactly, like for a given mass of water I can raise it's temperature to an exact fraction of progress along the way to boiling.  And I have the numbers on a variety of Fire Nation steam engine designs, so we can get an exact comparison on power, uh assuming you already have a good way of converting your measurements of your engine's power into weight moved through a distance within a period of time.  Ah, to explain, I think that is the most promising method for generally expressing physical power, although there was some debate over alternate methods and there are a lot of imperfect methods to express power as heat.  The power as heat thing is a point of nationalist pride even though I think it is kind of stupid because you could always make a more efficient engine.  In fact, the standard conversion ratios kept getting rewritten to match the conversion of whatever the current most favored fleet flagship's steam engine had.  Kind of petty and stupid really.  If you ever publish your designs and reveal even greater efficiency and leap past a century of Fire Nation scholarship (tainted as it is by ego and an overly pragmatic military focus) and your design becomes the standard heat-power conversion ratio I am going to find that absolutely hilarious."

Well, find it hilarious assuming he isn't dead at the hands of an Earth Nation mob, but he'll let himself dream for the moment.

"...Weight moved through distance... I've been measuring force based on the rotation rate of the wheel, and increases and decreases to it. Getting it to help move the cart without completely stopping the wheel was tricky. A spinning wheel is, actually, an object in motion though... If you imagine it as a lot of bricks tied to ropes going around, I mean, the motion of all the individual bricks added up would be an integral, but now I'm wondering how to calculate that, I've never heard of it thought of that way before... That kind of nonsense with changing standards is why I don't go to Ba Sing Se's academic circles for help. They're all up their own noses in studying the ancient tomes and smiling patiently at the insane nonsense their juniors come up with."

"Well, I like weight through distance for it's simplicity, and then using idealizations of simple mechanical tools you can convert it in a consistent way.  Like a lever, you have one end moving a longer distance with less weight to move another end a shorter distance with more weight!  And to convert that to rotation, you can consider the circumference of a circle, which works out consistently if you are thinking in terms of large gears and small gears and which is more forceful.  I didn't actually know the math for exactly calculating it for a heavy wheel with significant weight in the middle and not just along the outer circumference... but it sounds like the right integral might solve that!  Like dividing up the shape the right way."

"And the Ba Sing Se academics don't exactly sound pleasant to deal with, but I assume they at least don't challenge each other to lethal duels over the pretext of the engineering standard they are using."

"They try to embarrass each other at fancy dinners, which is considered much the same level of escalation, from what I hear. But yes, no lethal duels. Mostly. So how do you use weight through distance as a measure of energy, can you give an example?"

“Well I mentioned levers and gears, it applies to pulley systems and other mechanisms as well.  To outline some actual practical machinery…”

He gives several examples. His examples include a water pump (which leads into a diversion about the pull of the earth and weight, but the math still balances out), a machine to wedge and crack rocks open (which ran into limits of the metal’s strength and thus proved impractical), and several setups for propulsion of Fire Nation ships.  The basic principle is ultimately an extension of the same math as levers, shorter and stronger motion or longer but weaker motion, and exchanging between the two.  He notes you can lose energy to friction (which, fascinatingly, generates heat) but otherwise the equations balance out.  His explanations are somewhat hampered by a lack of writing material, but he can accurately recite specific numbers from memory.  He ties off his summary by bringing it back to the abstract and the question of the energy of heat.

“And in principle, if you had some theoretical idea of what and how a perfect steam (or in your case air) engine operated, you would then have a conversion ratio of heat to physical energy.  And you could do the opposite to get another ratio if you could optimally maximize heat from friction…but to be honest I’m not sure those ratios would actually be the same.  Also, I’m not sure ‘perfect’ engines would have the same theoretical conversion ratios for steam vs. air vs. more exotic substances.  Do you know if air expands linearly with heat like steam (once it’s converted from liquid water that is) does?  Do you know of any exotic substances that expand non-linearly?”

He does have half a dozen lap-sized blackboards for sketching, in terms of writing materials. He can follow along and then try to estimate some analogous examples...

"Someone who is not me and has more time and materials should do careful experiments on heat produced in various mechanisms and how it relates to force. I'm not aware of the details of how various substances expand and contract. I do know in terms of air it's not exactly... Well, you can force air into a smaller space with more force and pressure. It's more like the product of pressure and volume varies with temperature. That's the whole way my engine works, generating pressure, and thus force, under changing volumes. I must admit I'm considerably more interested in practical application than theory. For that, commonly available materials are best- Air, water, steel or brass, leather, and so on. My poor Fire Ox can't pull this thing at very good speed all by himself, especially up slopes or on soft ground. I have to engage the engine often there."

"For metals, they expand or contract by a linear amount, but it is obviously a lot less than steam does.  You can build some pretty neat thermometers by using two types of metals coupled and wrapped in a spiraling shape, and some important projects actually use these for consistency even though 'real firebenders can gauge the heat themselves accurately.'" his voice is dripping with exaggerated sarcasm.

"But ah yes as for practical matters... do you have an estimate of this cart's weight?  With that, and the incline, as well as bit of trigonometry, we could calculate how much energy the engine is adding.  I don't know as much about calculating for soft ground, it doesn't come up with water based propulsion.  I would imagine you could treat it sort of like friction or maybe drag in water, but the way soft ground can stick and cling and freeze up motion is probably a critical difference."

"Huh. That does sound very neat. I wonder if you could, say, have it pull a string and close or open a valve automatically if things get too hot? There must be other ways to do that too, I have a spring valve so the steam vents instead of exploding if I push it too far... Oh yes, a lot of energy is lost in friction and pushing against soft ground. I had to re-design this thing with wider wheels several times, there's just a strict limit on practical ground pressure. How heavy it can be for every bit that touches the earth. I also have to gear it very far down, turning the wheel's fast speed to a much slower but more forceful motion. The wagon, empty, weighs about fifty five, sixty dan*, but when you add all my furnishings and current cargo and myself and you it's probably... Closer to a hundred and twenty?"

*A dan is "a bag of rice" and is about 50-60 kg

"For purposes of getting numbers to do calculations from, maybe we could just record numbers while on harder sections of road?  Do you know from memory if there are any decently long sections of the road which are hard and well-maintained and have at least a slight incline?"

"The roads immediately around Omashu would be best for that, in this region, but we are heading in the opposite direction..."

“Well that question is more of theoretical interest than immediate practical application, and I can write down everything I know for you to collect and analyze the data on your way back.  In the short term, what matters most is how much efficiency I can add to your use of fuel and/or how much fuel I can entirely replace.  I have several possible techniques in mind.  At a wildly optimistic guess, (extrapolating from manipulating candle flames purely via meditation and breathing) I could keep your furnace at least at partial heat with a tenth of the fuel it would normally take, and do that as long as I can meditate.  As for a more modest guess as to what I could do with constant meditation… maybe somewhere between a quarter as much to half as much fuel?  Usually with steam engine’s furnaces I’m directly bending fire at the furnace and I can do that for an hour, maybe two if I’m pacing myself carefully.  With your furnace’s size, directly using fire bending could entirely replace the fuel.  But it’s smaller size means doing that way would be irregular in heat (spiking with each movement in fire bending).  As a third technique (probably not effective but worth testing), I could directly transfer heat (either from my fire bending or from the furnace) to the air within your engine.  Without a flame inside your engine’s chamber, this technique is probably too inefficient to be worth using, but maybe getting the heat directly where it needs to go would make up for that?”

"We should design such experiments and write it all down even if I can't implement them right now... Directly putting heat into the engine chamber itself would be counter-productive unless you can do it in time with the pulses. It depends on the cycle of heat and cooling. Or did you mean firebending on the boiler? I don't even use the steam except as a heat store and an enormously oversized kettle, hah. So that might work. If you can boost a low coal flame to a higher one, that will suffice. It won't be a quick journey."

"I could move heat out of the boiler into the air of the engine chamber.  And I was overlooking the fact I would need to time it with the cycle of the chamber... but actually thinking about it, I could move heat in and out.  It depends how fast the engine cycles, if I could match it to my breathing that would be easiest.  Hmm... it would be a bit of a stretch of my skills, but I could probably primarily boost up a low coal flame and simultaneously synchronize some heat transfer in and out of the engine chamber... it's probably not worth it compared to just boosting the flame, but now I'm curious about trying, if only for the challenge."

"It gets going pretty quick..."

He stares at the numbers again.

"...It'd be nice to have something with higher power. I don't think my type of design can go up that far without being impractical. I suppose there are always tradeoffs."

"Ah, I incorrectly assumed it was slower... maybe it's time that I see it in action then?"

A new type of engine!  It was definitely worth the risk exposing his secrets to this man to see it!  Well maybe he'll second guess that if he finds himself in a prison cell tomorrow, but for the moment he is too excited to worry.

Sure, he'll start the engine. "Look, it's already warm below and cool on top- I might want some of those metal gauge thermometers- So really all I have to do is set this to unlock the flywheel and this to disconnect it from the gearing to the treads, and then give it a-"

He heaves the big, heavy iron wheel clockwise, setting it spinning slowly, then grabs at it and pulls it faster a couple of times as the mass slowly spins up, the engine starting to cycle- "Just a bit..." 

The engine is now huffing and hissing along with a quiet huss-hish huss-hish noise, steadily creeping up from about a revolution every two seconds to something quicker. The whole air-displacing plate moves with it, too fast to firebend with unless you're going quite quickly.

"And... There you have it. The real challenge for me is regulating the speed and transferring all that motion to the wheels without shaking the whole wagon apart."

It's exciting to see.  He watches closely and starts trying to feel the heat within it.  He experiments with his breathing, trying to do multiple little partial breaths in or out in time with every other cycle, but even like that it is too fast for him to directly firebend the internals.  He tries to think of the problem from several angles.  Maybe... some wind instruments have techniques that use air stored in the cheeks to provide time to breathe in through the nose during a long continuous note.  Maybe he could do something with his cheeks at a faster timing than he can with his lungs?  Except the breathing in firebending isn't just about the air, it's also about centering and syncing the core of your being, and air in his cheeks just doesn't have the same power behind it.  Maybe if he could also use his cheeks to firebend?  Facebending isn't exactly something he's heard of before, but according to rumor the Dragon of the West can firebend on a combat relevant scale purely through breathing.

He's getting distracted.  He focuses on the warmth below, steadies his breathing, and very gently raises the temperature ever so slightly, just to get a feel for it.