We've done the first part of August, and it is very hot and very crowded. Most schools have not started yet, and a lot of families take that last vacation before the start of school.
On the upside, the parks are open longer and there are more things going on -- parades, fireworks, etc.
The very first week it is still very crowded. The later you go in August, the less busy it becomes, but the closer you get to hurricane season. About mid month, the crowds begin to drop off some.
We have visited the 3rd and 4th weeks of July the past couple of summers. It is hot and very humid and you can expect afternoon rain storms, but they usually don't last too long. We just throw on our ponchos and keep on touring. I haven't found the crowds to be unberable and we love the longer park hours.