I have been hunting in the heat for many years, as our bow season starts in September. Dress for the heat (and the bugs) and take plenty of fluids. If you have to trail a deer in the heat, you could be there a while, so the fluids are very important.
I sometimes start trailing a bit sooner than I might in colder weather, but a lot depends on how good the hit looks. I do not hunt much in the evening, because I don't want to trail at night. I am just not that good at it. If you need to track after dark, there are lights with filters, or you can use a Coleman lantern to help blood show up. Use the florescent trail markers to mark your progress. The meat does not last as long as it does in colder weather, so stay with it.
Once you locate the deer, field dress it and get it on ice quickly as others have suggested. The process is no different than hunting, trailing, and processing in cold weather, except that time is much more crucial.
One thing you just don't get used to is that deer hunting with sweat dripping off the end of your nose just doesn't feel right. Man, I wish bow season opened in October with gun season beginning in November the way it used to do when I was young.