It seems to me you have a mixture of what my dad and I have. His hands and feet are always red hot. Mine, on the other hand, are always cold, sometimes to the point of my nails getting purple. When the temperature outside is cold, which is not often since I live in the sunshine state, my hands get hot. I feel like those heating pads that have to get really really cold before they get hot. My dad found information about his problem, it is called Erythromelalgia (EM) although I doubt that this is what you have I hope this can be a start to finding out what it maybe. Let me know if you find any information!

By the way, here is a site about EM http://www.erythromelalgia.org/tea/skins/c ms/viewpage.php?pname=What is Erythrom elalgia?