In 2011 we went that week. It was HOT. Very hot. I am from Maryland. I am used to heat and humidity in the summer but expected it to begin to cool down by the end of September. It did not. It rained 2 times while we were there. Both in the evenings but not overnight. I think as long as you are prepared for the heat you will be fine.
We had family visit us that week from Sarasota and they commented that we did have a freakishly hot week so maybe you will be lucky. The coolest temp the week we went was about 95. Take advantage of water rides and free ice water. I wouldn't totally rule out going that week again but it has definitely ruled out any chances of us going in the summer ever.