Thanks everyone for all your help! Ordered some cooling neck thingees from
Amazon. Plan to stop and drink lots of water. Will go to GS and ask if they have advice.
MamaBunny, I have been around for a while but just didn't have this particular problem.

When my daughter asked her neurosurgeon about the trip, she (doc) said be careful of heat because of seizures. Kind of a different world, kwim?
Yes I do! It changes how you do things - but overall, WDW is still a great place to vacation with any kind of health problem, simply because they are (in my opinion, and experience) the best at creating a welcoming environment for Guests of all kinds.
I know you already know - but remember that the First Aid stations at each park will be your friends. Any time she is feeling overheated, head to a First Aid station and let them know why she needs to cool off for a bit. They will have quiet, dark cool beds (with lots of ice packs!) and it could be that by simply taking strategic cooling breaks, combined with other strategies, she will do well.
I have this "super-fun" (not!) allergy to the sun, which means that any time of year at WDW is pretty much toxic for me LOL. I have a battered old parasol I got at the China Pavilion in World Showcase that I bring with me on every trip, and I basically wear rash guard shirts and long-length UV protective gloves (also from Amazon) to help stay cool. Both the rash guard shirts and the gloves are "cooling" when you spray them lightly with water. Most importantly, focus on the lightest colors for clothing: white is best, pastels are good too. Old school seersucker (if 100% cotton) can be great too; those little "puckers" create tunnels to move air through the garment and help keep you cool. Avoid long pants and denim if at all possible - they just seem to trap the heat and humidity.
Of course, sheer cotton or linen is great (but can be see-through if soaked on a ride!) the main thing to remember on dressing is air flow.
Sandals are best (especially if she will be sitting in a mobility device) because you can feel 10 degrees color just taking off your shoes on a hot day! If she does sit in a mobility device, remember that upper legs/thighs get much more sun exposure when sitting all day, so white/lighter color pants are even more important. If wearing shorts, don't forget to apply sunscreen to the upper legs as well!
Take along some inexpensive cotton bandanas (you can find them for $1 each at Wal-Mart or Hobby Lobby) that you can dip in cold water and press on pulse points, or just use to wipe faces and feel a bit cooler. As you probably already know, every QS gives away cups of ice water for free. Small battery operated fans are wonderful - be sure to keep a replacement battery on hand!
A lot of heat-sensitive folks will utilize Park Hoppers, and may do a few hours in the morning at one park, during the heat of the day they retreat to the Resort to nap or play in the pool, then head back to the parks when the sun has started to create longer shadows.
Remember that, ironically, at night things can cool off a lot, so a lightweight wrap might be good to keep on hand after the sun goes down if she is subject to getting chilly. Again, this is especially true if you are sitting on a mobility device; because you aren't moving (walking), you don't create the body heat that an ambulatory Guest does.
If you think about how folks stayed cool during the summer months in the south before there was air conditioning, it might help you strategize!