Native here.
September is probably one of the hottest months. Not only the actual temps (going from high 80s to high 90s), but don't forget to factor in the humidity. This is not a dry heat; it's moist, and will often add 10 degrees to whatever temp the weatherman says. We call this the heat index. So a temp of 96 will have the heat index (or feel) of 106.
The times from around 11:30 a.m. to 2:30 p.m. or so are brutal. Try and be inside or wet as much as possible during these times (stores, rides, pool).
We tend to have afternoon thunderstorms generally rolling in around the 3:00 p.m. - 4:00 p.m. time. They usually don't last long, tho, maybe half an hour or so. However, respect these storms! These are not "Up North" storms. There is a ton of very serious lightning. Get indoors. We generally always plan on being back at our hotel in the late afternoons to freshen up, shower and change before heading back out to the parks or nightlife activities. Epcot is a good place to be during a storm since there's so many stores to duck into, too.
Plan to sweat...I'm talking dripping wet. Wear clothes appropriate for being wet either from sweat, rain or splashes gleefully welcomed from water rides.
Carry water with you at all times. I cannot stress enough to keep hydrated throughout the day. Drink when you are not thirsty. Even locals carry water during the day in their professional lives (come on down to the courthouse and see all the lawyers carrying their briefcases and water bottles on the street).
The only other weather-related item I can think of is to watch for hurricanes. We get notice of them, and hotels at WDW or USO are generally a good place to be. Obviously, September is a time to be flexible with arrival/departure dates due to the 'canes. We've had to extend or delay a couple trips in years past (we're two hours away, so it wasn't a big deal) due to 'canes directed at our hometown, Orlando or somewhere along the path we take to get to Orlando.
HTH & we'll be there sweating right with you!
