Dave,
IMHO having an AC sleeping facility is a mistake; it keeps him from climatizing. I'm saying that based on my experiences in Somalia in 92 - 93, where it got even hotter than that. (And FWIW, my experiences living here in the humid and hot Midwest summers). For a brief time I had the use of an AC trailer and working outside became miserable. When I moved back outside 100% of the time, I functioned great, slept great, etc. Sure, you sweat a lot (and have to drink a lot of water), but it was not that hard to get used to.
Spending time in and out of AC space is the problem.
HTH,
Tom