think of the school nurses office from elementary school only bigger and better. (cause what isn't better at Disney!?)
They can store medication and medical equipment for you during your day. (just like the school nurse)
They have cots in curtained off 'rooms' (three walls one curtain). It is a/c'ed.
My daughter was starting to show signs of heat exhaustion, so I went in and asked if my daughter could just lay down for a little while. there was a chair in the room with the cot, and they had a water cooler as well, the nurse suggested I get her to drink some water. At first DD wasn't feeling up to it, but after about 20 min she finally felt up to drinking water. Before we left the nurse offered to give her a Gatorade, but my kid wouldn't drink it and neither would I.
First aid is just a great place for quiet too. I could have easily fallen asleep while my kid was resting.