We went that exact same week last year (2009). And it was hot. We had to go take naps in the afternoon, which was a first for us. And it wasn't just the kids who needed a nap! :lol:
As for crowds, that is the end of Star Wars Weekends, so DHS will be crowded Friday, Saturday, Sunday (June 2,3,4) but we went during the Star Wars Weekend and had a great time seeing all the tourists and locals in costumes, the special Star Wars parade, etc. It is also Gay Days that weekend (June 2,3,4,5) but that had no impact on our trip at all. The one piece of advice we followed was to avoid the MK on that Saturday (it will be Saturday the 4th for you) because that is the most crowded day of Gay Days (makes sense - it's the most popular park and I'm sure a lot of people come down just for the weekend, etc.) As I said though, it had zero impact on our trip otherwise! I thought the crowds were just "medium" sized. It wasn't empty in the parks, but other than those 2 weekend events, it wasn't crowded either.
Hope you have a great trip, whenever you decide to go!!! :wave: