I went once in April (well I have gone more then once in April but back then it was just the MK & maybe Epcot).
We went the week before Easter. We arrived on Saturday, Sunday was Palm Sunday & it wasn't so bad. I noticed the crowds picked up by Thursday, Friday & Saturday I did something that I never did before...I left the MK at about 10pm & they were open until midnight or 1am.
The lines were HORRIBLE! I vowed to never go during spring break ever again and I haven't.
That was in 1999 (we got engaged there that trip). We (my family pre marriage) had been going in the summer-end of July/first week of August for quite some time. Yeah it was crowded but it wasn't like Easter week.
So I vote for July. Although I went in July in 2005 and it was the hottest trip to WDW I had ever been on.
FYI, with the heat, go early, leave at lunch time-take a nap, swim, laundry...a break basically. Then go back around 5 til closing. We have been doing that for years and I trained my husband that way too. We also make sure we do not go to a park on the day we arrive or leave & we take at least 1 if not 2 days off-pool days.