I'm from FL, and people living in FL still live in FL in August too. It will be very hot and very humid in August, but go ahead and enjoy your holiday as you have booked it. Start out early, and take a siesta/swim in the afternoon, and then do something later in the day.
However, totally agree with expatinscotland about the Everglades. As I said, I'm from FL, and we never went there except from Oct. - Feb. Expat..we always used to say Houston was even more unbearable than FL...it's usually selected as having 'most oppressive weather'...you know what you're talking about.
Also, is chance of hurricane, but they're usually a greater chance in Sept. ..whatever that's worth. It's raining here too so don't bother about the rain..you will WANT it to rain in August..probably won't all day, but you will do a 'raindance' for some to 'cool' the air off...actually this just makes even more humid.
Take lots of insect repellent..I mean lots. I guess if I were you, I'd go ahead and do the Everglades for ONE day early in the day and then get over to Naples and get in the A/C.
I don't think they even rent cars in America that don't have A/C, but make SURE you get one that does. You will be sweaty and feel 'icky' but will be okay after a nice shower and A/C..well until you have to go out again...but use that bug stuff..if what you get doesn't work, buy another brand