Hi Sideshow bob,
My kids and I live in So CA and visit Disney every couple of months. If you go to Disney's City Hall ( just to the left, as you enter the park and go under the train) and get a Guest Assistance Card. It will allow your daughter and five other people to either go in thru the rides exit, or go in thru the handicap entrance, so you can skip the long hot wait in lines. They don't ask for a lot of details regarding the condition, but Instead of trying to give a whole lesson on dermatology, i just simply tell them "my son over heats easily and cannot stand in hot lines for a long time... What a fun surprise for your daughter! Let me know if you have any other questions:)
BTW~ there are also locker you can rent for $6 per day. I usually bring frozen waters and gatorade and keep them in the lockers with snacks...