We have been two times around the second week of June. The crowds can be towards the heavy side, but with planning and fast passes we did not have any long waits. As you can imagine, it can be hot, but on our second June trip we arrived to a little rain on Sunday but after that the next few days were actually dry and very comfortable.....unusual but great.
We had E-nights when we went but they will probably be replaced now with the new EMH. Take advantage of the extra hours, especially in the evening. It's a lot more comfortable without the sun beating down on you. We always took a hotel break around noon, just as whatever park we were in started to get really crowded.
Read these boards for a lot of great info. With planning you will have a great time.