My family as always gone in June or July up until last year, so I almost feel a little off when I go and it's NOT summer. Like others have said, it will be hot and more crowded than you're use to, but you'll still have a fantastic time. I would suggest the following:
1. Take advantage of rope drop and morning EMH (we've never done evening so I can't speak on them, but I'm sure they would be useful as well in dodging some of the crowds). In the off season this isn't as important, but it's our main game plan in the summer.
2. Schedule your FP+ selections for late morning/early afternoon, when the crowds are starting to grow but after you've done some things via rope drop. Or sometimes we just schedule them all for whichever park we're going to in the evening.
3. Take a mid-afternoon break. We usually leave whichever morning park we're at by 1 or 2 at the latest and hang out at the hotel, go to the pool, take a nap, etc. Again, in the off season this isn't as important, but you'll definitely want a break from the people and the sun. We then usually go to whatever park we're having dinner at around 5 or 6.
6. Frogg Toggs chilly pads are a fantastic way to give yourself some relief from the sunshine. It's really not as bad as you may think, though. Yes, it will be hot, but Disney does such a good job in terms of providing shade, and most of the ques have air conditioning.
I think the most important difference between going in the summer versus going in the off season is the need to stick to a plan. When we went in February we were much more able to sort of go with the flow, re-arrange FP's, etc. You'll need to be more committed to what you've planned ahead of time in June, at least for the most part. You'll have a great time though!