And is Professor McGonagall there?

She is! She has gotten the wall back together, but the portrait hole no longer has a portrait on it. The portrait is on the floor, and the fat lady in the pink dress is as still as, well, a painting. She's gone back to futilely trying to destroy the diary, which is now in a different, significantly thicker box on a table now sporting several injuries.

"Do you want me to try?"

"Please do. I have made Miss Weasley as comfortable as I can, but I can't release her until I've severed the connection."

How would this book like to share all its space with a similar mass of liquid nitrogen?

Now it's in a puddle of liquid nitrogen! Now it's in a vapor cloud. Now it's fine.

"I can start trying assorted acid or I could - if I can work around whatever went wrong with my computer - take it into space and feed it to a tiny black hole, but I'm not sure if I should expect that to work where interpolation failed."

"Electricity doesn't work in Hogwarts due to magical interference. I have already tried acid, I'm not sure what a black hole is . . . . Hm. How much ice can you create, how fast?"

"A lot? Uh, I think it's something like two hundred cubic miles per second at absolute top speed but I should not do that under most circumstances because it's hard to stop in the middle with suitable reaction time if you're going that quick, that's astroengineering speed."

"And you could create it in whatever shape you wished? For example, in a hollow cylinder, continuously renewed?"

"Sure, assuming it doesn't exceed my range which is a couple astronomical units. Uh, and I guess depending what you mean by continuously renewed, that seems like it might depend on whether any forces might change its direction or anything like that once it's made."

"In that case, if you are willing, we might be able to safely make use of Fiendfyre. It is a form of magical fire which can destroy even very strong magical protections. It is, however, extremely difficult to control. I would not ask you to do this if a student's life were not at stake--I believe the diary is draining her life force."

"Okay. Possibly, uh, not in the school."

"I was intending to use the lake."

"Sure."

Then if he's ready to do it now, they can traverse Yet More Stairs, and also 540 degrees of clockwise hallway with no apparent elevation change, and emerge via an elaborate entrance hall into the Hogwarts grounds. They're very picturesque, with an imposing old-growth forest on one side and a large lake on the other.

"Okay, how do you see this working?"

"You make an open cylinder of ice near the shore, I levitate the diary in and cast Fiendfyre, you seal the cylinder and keep replacing the ice until I can put the fire out, which I expect to take not less than twenty minutes and not more than two hours assuming it remains contained within the cylinder. With your permission I will cast some protective spells on you first." She directs her wand at herself, then at the Lakeshore, murmuring more not-Latin.

"I don't object, since I don't know how magical damage might interact with my being indestructible." Big ol' cylinder of ice.

McGonagall casts the protective spells on Cam, and summons a broom so she can see down into the top of the ice cylinder for better aim.

She tosses the diary in, hovers well back, counts down "Three, two, one, now."

And there is fire, white and gold and incredibly hot. Cam can feel the heat on his face from here. Ice starts flashing into steam in moments, and glowing through the steam cloud are the firey shapes of beasts and monsters, clawing at their icy prison, roaring, boiling their way out.

Freaky!

Cam tries switching to dry ice after a bit, ready to go back to normal ice if anything weird happens and wishing he'd asked about this possibility first.

Nothing freaky happens beyond what was happening already.

McGonagall starts fighting against the spell from pretty much the moment after she casts it. The flames slowly shrink, then flare up nearly as large as they started, then shrink again. She looks gradually more and more exhausted, and by an hour in she's started to slump down on the broom, but she keeps her wand pointed rock steady at the fire.

"Do you want... coffee or something...?"

"Coffee . . . would be . . . lovely!" She calls. It's clearly an effort to make herself heard over the fire.

She can have a lidded to-go cup of coffee with modest quantities of cream and sugar in her free hand, appeared slowly so she isn't startled into dropping it.