If this were an earlier era in the history of the Eastern Empire, there might be enough mage-Thoughtsensers that Altarrin could select someone brilliant and experienced at magical research to eavesdrop on their visitor's mind. Just to learn more, faster. If at all possible he would still compensate her later for anything he learned that way, of course - and it's not even that he doesn't trust her to share her knowledge, it's clearly up to him to give her the right incentives and he's confident he can do that–
It's the present era, though, when he has only a small handful of Thoughtsensers and Ellitrea is exhausted, and so Carissa's current thoughts, whatever they are, will go unobserved. There's no point in dwelling on it.
Altarrin is still having a stupidly difficult time focusing on his neglected work. He keeps finding himself sending over more instructions to the guards via the communication-spell artifact. Even though he's not worried that their 'political prisoner' is going to try to run away.
...He's worried about her safety. Which, on the surface, makes very little sense - she's in the Palace behind all of the usual protective wards and then some, he has guards who he personally trusts watching her, and hardly anyone knows that she exists let alone how interesting and potentially valuable she is.
It's just– well, he's failed to save a lot of people. And it's feeling very salient, right now, that the people he's failed to save are disproportionately those who left him feeling the way he does right now, about this woman from another world. That she's bringing something new to the table, that he's never met anyone quite like her before - that there are a hundred different plans he could start to prepare, but he wants to wait, because they'll be better plans once he earns her trust and can have her input.
Altarrin is pretty sure that it's unstrategic to let this distract him, right now. Their visitor is very hard to kill or even injure badly, he's seen that himself, and he has no reason to think that the gods can respond quickly to something like this.
....He still hasn't properly slept since yesterday, which is predictably not going to help.
He passes on a few more contingency-orders to his mages. Writes a report, locked with magic so that only the Emperor can read it. Catches up on the most desperately urgent tasks in his backlog.
And then puts up some additional wards and shields on his office, pulls out a bedroll, and falls asleep on the floor.