He's...hard to Thoughtsense, not in the sense of pushing through shields - he is very cooperatively not shielding at all - but in the sense that it feels like there's three times as much thinking going on as what normal people can manage, in layers and spaces that wouldn't even fit into most minds. And it's not just the volume; it's going by so fast, impossible to keep up with.
Altarrin is clearly trying to make himself legible, though, holding some thoughts 'closer to the surface' and making them more explicit.
He has a lot of concerns about the tactical situation in Oris. The grand simplification of why is 'because it will obviously advantage the gods if the Empire comes out of this weakened rather than strengthened', and a flicker of - places where there's room for the gods to maneuver, places where the Empire is currently leaving outcomes up to chance (which will never be in their favor) rather than pinning them down and overdetermining that they're going to win.
(A deeper level of thought, at a preverbal level and quite hard to pick up on: that the Empire's entire strategy relies on always overdetermining that they're going to win, and this is...not doomed, necessarily, but certainly a very very big ask, and one that will predictably not always be met.)
He's thinking ahead about how the artifacts they're studying here might be used in the various wars. There's a sprawl of hypothetical plans, weighing the pros and cons of each - this part is just logistics, but even with a fraction of his attention it's clear that he's tracking way more possibilities and risks than most people can hold.
(The implicit thought below it, that actually he doesn't want to be fighting those wars at all, is barely perceptible, and comes across mainly as an emotional overtone of...weariness, and heaviness, and wanting it to be over.)
He's thinking about Iomedae's world - a tangle of inferences, there, what can you predict about a society and culture from the handful of facts he knows about their gods and their afterlives and their style of diplomatic letters, what does that mean about how to approach trade with them, or war...
He's thinking about the problem of Gate planar routing. This is actually where most of his attention is, and it's the hardest for him to make legible, because it's nearly all entirely nonverbal mathematical-spatial intuition. He thinks it's solvable, optimistic estimate he could do it in a few days with the headband, pessimistic estimate a week, pessimistic estimate if he decides to remove the headband is...longer but he can still get it, a month maybe.
The emotions associated with that are also the ones at the forefront. Determination, and anticipation, and uncertainty and fear-of-the-unknown mostly held at bay by the relentless drive to move forward. They need this.