When I was growing up, our family trips were always in August because of lower crowds/prices and NYC schools going back later than the ones down south, and I have been back a lot for Labor Day weekend trips as an adult. tbh even now I don't find the weather in FL to be any worse that time of year than at home. The actual real feel temps are about the same. It can get very humid in the city in late summer, as bad as sometimes worse than down south.
But it really does depend on how well you handle heat. I swear I'm built for it, doesn't bother me at all (dry or humid!), but some folks just can't cope no matter what they do and think no one else can (see some PPs). The key, like many folks have said, is staying indoors during that hottest part of the day. You don't want to be in the parks that time of day anyway because it's the most crowded with the worst waits. I still use the tried and true strategy of rope drop till about noon, long rest at the resort during the middle part of the day, then go back in the evening after the clockwork afternoon thunderstorms and close out a park. When you are outside, go slower, switch off between indoor/outdoor attractions, make sure you are hydrating enough (Liquid IV is a godsend) and taking breaks. The latter two are always important but become even more so during the summer months.