I'm the same way. I either wear knickers or shorts that look like bike shorts, but without the chamois, or a running skirt. I always wear a sleeveless top when running indoors. I have gotten in serious heat trouble running at home on my treadmill and not putting on the room AC or opening the window in the loft where my home gym is. Even in the winter, or in the summer if it's raining out and the central AC is on, I need to do this. After I had to sit down on the floor and put my head between my legs from almost fainting, I realized this had happened a few times either at the gym or at home and it was heat related. Somehow, I built up to riding in heat, but I can't do the same with running.