I grew up in Chicago - HOT and HUMID with only polish air conditioning.
Get window fans - beg bought and steal them - put bowls of ice cubes in front of the fans. Put some wet towels in the freezer too so you can take them out and hang them on a cair or something directly in front of the fans.
Trust me - this will help you sleep at least.
It's currently 73 in my office and I have the heater on! I am always freezing!