We are going in early June - our first ever summer visit. I've been in central FL in the summer before however, and it can be brutally hot and humid - especially midday and early afternoon. Our plan is to hit the parks at opening - go back to our resort(very close offsite pool home) at noon or 1, hang at the house or by the resort pool, and then return to the parks late afternoon/early evening.
I would suggest light fabrics and light colored clothing(white/light clothes absorb less radiant heat), hats, sunscreen, staying hydrated, staying in the shade when possible, air conditioned shows/attractions in the afternoons, etc. Common sense and not trying to overdo it will be your best strategy. Your feet actually aren't a big problem when it comes to cooling. Most of your body's heat is given off by your head, torso, etc. As your head, legs, arms are generally uncovered, they are free to liberate heat mostly via evaporative and convective cooling. Wearing light airy shirts/tops is therefore a good idea to help the torso get rid of some heat as well. Comfort and blister prevention are bigger problems with the feet and wet feet can be a problem. If you get your socks/shoes soaked on a ride, wring the water out of the socks and pin them to a backpack to dry. Good sandals like Teva's are great but DO NOT forget to sunscreen the tops of your feet.