Only been a FL resident for 2 years, but the real humidity seems to start later in June, so you may get hot but not so humid (crossing fingers).
If the summer showers have started (we are in desperate need of rain right now!), there are great places to go in each park to wait out the rain:
-AK-The lion King or Finding Nemo shows. Or...if it still running (no lightning) - Kali River Rapids (you are going to get wet anyway!)
-MK - Space Mountain (queue is indoors) or Carousel of Progress are good choices. I like a break (upstairs) at Columbia Harbor House best. Head there before the drops start to fall to snag a snack/lunch and a table!
HS-Tower of Terror, Toy Story Mania., or Rock N Roller Coaster have covered/indoor queues. Or try one of the indoor shows. This is my least fav Park in the rain!
- EPCOT-The BEST place to head when you know the storm is going to start-the aquariums in the Seas pavilion! We love that area and can easily wait out the rain and not feel like you are missing a thing! EPCOT in general has nice, big pavilions to wait out rain (just be sure to be inside once it starts because "darting" to a pavilion in Future World can get you drenched since the open plazas are so large between them!) Even the WS has great places to hang out inside to wait out the rain-movies in the countries of Canada, France or China, Mexico's indoor marketplace and boat ride, etc.
Have fun...take breaks...do not let weather (sun/rain/heat) dampen your spirits...just remember to drink fluids, wear hats and sunscreen and take A/C breaks.
Have a magical trip!!!!!