It sounds like poor circulation. Have you tried doing cardio? I find I keep warm more when I exercise regularly, than I do when I'm sedentary. I could cope with that temperature if I was lying down, on the sofa, watching TV, but would break sweat if I did something. Admittedly, 15°C is a little cool for me lounging on the sofa, so I sit in a sleeping bag, but then I get too hot, so I unzip it. I can't see myself ever living in a hot climate. The heatwave we had the summer just gone was torture. It got to 38°C, at high humidity where I live, so I found a nice cool river and went for a swim.
I can confirm that doing cardio does help a bit, with the same effects you describe. (As does being in better shape in general. Higher resting metabolism, etc.) I really need to start going to the gym again, even though it's something I have never managed to enjoy doing. :/
(I am OK with hot weather though, since I grew up in a place that gets plenty hot in the summer.)
It might be worth getting your doctor to check you for Reynaud syndrome (if you get colour changes). Mind you, the main treatment is keeping your fingers and toes well covered, although there are drug treatments for more severe cases.
Hmm. I don't get color change, so I don't
think one could say I have this. But while reading the wiki article about it, it did say that ADHD meds can exacerbate it, and so that might partly explain it in me. (It also said that some joint and connective tissue disorders can cause it, and given that I do have sensitive joints and tend to scar easily, both of which are symptoms of some of those disorders, I suppose it's possible that I could have a mild case of something like that.)
I also have a pet theory that my hands and feet feel cold because they're giving off tons of heat, thus losing it. (Many a partner has told me that I am an oven in bed, radiating tons of heat.) :p When I first go to bed, I frequently have to cycle between sticking my feet out to cool them, and pulling them back in because they get cold, until my body temperature has begun to drop and I've reached thermostasis with the bed.