your feet and your head heat excapers and on a work day youe feet produce about 3 cups of sweat. You could be over heating at your lower body and you could have low blood pressure so it all come out your feet. Is your bed slanted. maybe if you sleep the other way it could help.
Perhaps this is related to your job or other activities. Do you stand or sit for long periods or go jogging? Your skin could be reacting to the chemicals in your shoes, slippers, socks or nylons. While at work (if possible) remove your shoes to let your feet breathe.
Because of my chemical sensitivities I have to wear 100% cotton socks and wear shoes that breathe to keep my feet cool. Most of our shoes are made from chemicals in one way or another even leather ones which is what I have to wear. I change my socks twice a day. I also have only organic cotton bedding which has made a big difference while I sleep.
Before you go to bed at night try soaking your feet in cool water (not ice cold). If what I have suggested doesn't work, you could see a podiatrist to check out other possibilities.