The courts are much cooler, and the Notorious Dame is essentially air conditioned (magically).
When humans/elves/mortals get hauled before a demon prince, it’s typically in the courts, and typically at the Notorious Dame. That’s also where the most of the dungeons are (there are multiple ones, of course) the temperature has to be at least livable for the toys in the dungeon (humans/elves/etc). A good sweat is nice, expiring of heat stroke before you can rip out a single toe-nail is not useful.
I don’t think it’s giving too much away to say that when Lillith realizes that the demon that caught Talarius and stole mana from a god is the same “Tom” demon that Antefalken’s been talking about, she will invite them for a visit/a stay. One appealing thing would be that there, Talarius would be able to get out of his armor.
And, assuming (not saying it will happen) they go there, Lillith will probably want to corrupt Talarius/seduce him…she’d need him in peak operating form, if you will.