Pretty much hot (95 or so) and wet almost every day for a little while anyway. Just bring your ponchos and you'll be fine. When everyone else clears out just march on!
This time of year is pretty much High humidity, so you need to have clothes that will not chafe you when you are damp. The other thing the Op was mentioning was the average daily afternoon thunderstorms. They usually don't last too long, but loke the OP advised BRING ( don't buy at WDW) enough ponchos for everyone and just keep on keeping on If you decide to buy at WDw be advised you can easilylose one of your party because they will blend in with everyone else who bought theirs onsite and they are MUCH more expensive.
HOT, HOT, Oh and did I mention HOT, especially at Animal Kingdom with all of the vegetation. I haven't been to EPCOT or MGM during the summer, but AK was really hot, MK not as bad because it is more open. You would think since I am from the South, I would be used to it, but I'm not. We were there for 4 days in June 2005 and it didn't rain until we were leaving to return home, and June is Florida's rainiest month. Take LOTS of sunscreen the Florida sun is bright