I feel cold all the time, but sweat like a guy?

I literally have to walk around in a heavy cotton hoodie if it's less that 80 degrees outside, because I'm freezing. Yet I sweat like crazy at the littlest thing once it gets over 85 degrees (at that point, I usually go for a tank top, but I still drip sweat just from standing outside). I've been told I have hyperhidrosis (an excessive sweating disorder) by two doctors, but it seems like it must be a basic temperature regulation problem. Also, I run for about an hour a day, do a Pilates class everyday, and pretty much live on fruits, vegetables, grains, beans, and salmon. I don't know how much healthier I can be, but I'm up for suggestions as to what this is and what I might do about it.