I too get hot fast while running. Here's the advice I got from my coach: Take water. Use it to cool you off as well as to drink---i.e., pour it over your head, or put cold wet sponges under your bra straps, or wet a headband periodically, etc. And do slow base runs to build heat tolerance--keep your heart rate low and don't try to go as fast as you can.
It's a work in progress for me. Will let you know how it goes.
"My predominant feeling is one of gratitude. I have loved and been loved;I have been given much and I have given something in return...Above all, I have been a sentient being, a thinking animal, on this beautiful planet, and that in itself has been an enormous privilege and an adventure." O. Sacks