We were there in early June....6/6-6/15. It was hot, but I expected it to be unbearably hot, so relative to my expectations it wasn't that bad. Our kids were 8, 4, and 21 months, and I was a little worried about the heat and the 21 month old since (a) young kids don't handle heat as well---especially chubby little guys, and (b) he never stays still, but he actually did fine. The plus side was that it was great weather for swimming and water parks. The crowds were manageable too.....we took advantage of Fast Pass and followed all the trip planning guidelines (e.g., take advantage of EE and then leave late morning for a break followed by a return to a different park), and it worked out fine. I do think early June is supposed to be a little more manageable as far as Summer months go. If you have the option of May though (excluding the holiday weekend), I'd go for that.....weather would be better and crowds should be much better since school would still be in session in many places.
Have a great trip!