My normal body temp is also low, and there have been many times it's been 97. something when at the doctor. As far as I know, my thyroid is fine.
I don't like being hot. I think it comes from living in air conditioning for 23 years. I had no issues adjusting to the cold when I moved back here, but now, it bothers me a little, mostly when I am running to the office from the parking lot. Never, though, when I am exercising! In fact, I prefer being outside in the winter to exercise. And, it's mostly wind related. I hate wind, even when it's warm out!