Go early, escape before noon, relax, have pool time, nap, then plan dinner in a/c then go back to the parks after dinner when it's cooler.
It is really hot and humid in September, so staying out of the parks during the hottest part of the day is my best advice.
Also, use cool crib sheets to cover the stroller, bring baby corn starch to powder the sheet a bit each time you change her or take her out of the stroller.
Obviously very light weight outfits, cool little dresses as opposed to shorts and tees. (Dresses are cooler and have those little diaper covers).
Stop for fairly frequent bathroom breaks to change her in comfort (the bathrooms have a/c) and keep cool water in her extra bottles.
If I think of anything more, I'll be sure to add it.