We usually go in early Apr or Oct. Weather is pleasant in the 70s, nice for touring and swimming. This year we went in May and it was too hot for us!!! Temps in the 80s and low 90s. I just can't imagine the summer (well I can, I went in August before kids once)
With the new EMH schedule perhaps you can plan on sleeping in, hanging out poolside and doing your "day" at night at the parks. The other option is to go early, come back and swim/sleep throught the heat of the day, and then go in the evening.
I just melt in the heat, lose all my energy so quickly....I can really relate. My personal tips are that I carry one of those little fans, drink plenty of water, take advantage of ac shows/eating areas whenever I can and just do not push it!