When you use AC during nighttime you never get adapted to the heat. Try slowly phasing it out.
I'm not saying it resulted in quality sleep (as a Canadian - I set the thermostat to 13 degrees in the winter when sleeping, and my ideal temperature in the summer is about 18 degrees) - but you get used to the outdoor climate reasonably quickly (in my case, about 4-6 months).
This is mostly a meditation on the fact that I used to be able to sleep in temperatures of 26-27 in Singapore. The human body (at least this one) can definitely acclimate to local environments given some time and exposure.
Of course - no acclimating whatsoever will help you if the wetbulb temperature gets up to 35. You are just dead unless you can find some active cooling at that point fairly quickly.