Usually September weather is very hot, with a shower around 3 or 4 p.m. each day. The storms can be a downpour, or just a little shower, but things at WDW just keep on happening anyway. The parades continue and so do the rides.
Be sure to bring a rain poncho every day, even if the weather looks as if it will be perfect. We joked that it rained every afternoon, but as it turned out, we were correct. The one time we left ponchos at the hotel, we were sorry!
The rain can help clear out the water parks and pool areas though. If you wait it out, a lot of people leave and don't return.
The evenings cool off a little, but can be warm and humid until late at night. Soemtimes there is thick fog in the early morning, because of the high humidity. It burns off early though, when it begins to warm up.
When we go to WDW in September, we take a break at our hotel pool or take an afternoon nap. You really feel so much better if you cool off in the afternoons and take a slower pace in the parks. Even though it is warm in the evening when you go back out, you are refreshed.
Be sure to drink LOTS of water, too. Dehydration can do you in quickly!