We were there mid-August last year and as it was our first full-summer trip, I was worried how we'd deal with the heat. I had a friend who'd gone the previous August and suffered terribly. Granted, it was a heat wave when she was there. I was surprised that it was much less of an issue than I expected. I had planned a bit longer trip (10 days) just for that reason, so we could take it slower and take breaks, and that really helped. Getting inside out of the worst heat of the day was good. And really, even in the parks you're inside a lot, unless you're walking around Epcot. I will say acclimating is a good idea - we don't have central air conditioning in our home, so we're pretty used to summer weather.
The thing about the fan-misters and neck wraps,
cooling towels, etc., is that I feel cooler if I don't have to lug all that stuff around. If it's very humid and you spray yourself, it might feel good for a moment, but then you're wet AND hot, and you don't ever really dry off. One thing I did find that I would definitely buy again were some little packaged Cool Off Towelettes. I think they were witch hazel with some kind of eucalyptus or menthol in them. I had my doubts, but they did give a very cooling sensation, and freshened us up too. And they were small enough to just stick in a pocket.
Don't worry too much. If you don't have health issues, just make sure you hydrate and wear sunscreen, don't push yourself, and when someone needs a break, nip into the AC for a show or a snack or shopping.