I think I'd much rather have an injured hip than be taking meds that make me heat intolerant....
Injured hips can be looked after and mended - chronic illnesses are yours for life. Back to the point...
put some ice cubes in your water bottle to keep it cooler
see if you can plug a fan in near the treadmill - if they don't have one then take your own
go to the gym early in the morning if you can when it's cooler
wet your towel so that you can wipe the sweat off with something cool
as for the session - I guess you could gently warm up and then do hill reps on the tready - you'll be knackered in no time - or do a speed session if the tready is fast enough: 5x1min @ 16k with 2 mins rest or something.
Sorry I can't help any more.
Good luck.