As it happens, recent threads have led me to read up on temperature regulation. I’ll summarize some relevant bits of what I’ve read, then speculate recklessly.
Body temperature regulation is directed by the hypothalamus. It secretes hormones that trigger various temperature-adjustment activities in the body based principally on two factors: blood temperature (which it senses directly) and skin temperature (which is relayed to it by the reticular formation).
Obviously, skin and blood temperatures can and often do differ, sometimes for reasons unrelated to temperature regulation. (For example, if you’re scared, the body tends to restrict blood flow to your skin and extremities–metaphorical “cold feet” may well cause literal cold feet.) When the two sets of temperature information are at variance, the hypothalamus has to weigh the importance of each. Logically, one would expect blood temperature to be weighted more heavily, and for what it’s worth, I found a study that seems to me to suggest this in rats.
That doesn’t mean skin temperature gets ignored however, and–WARNING: here begins speculation–it’s likely that it’s a proportional analysis. That is, the closer your blood temperature is to the hypothalamus’s target, the more weight is given to skin temperature. So, if your core temperature is right, you should be able to strongly affect the composite perceived temperature by relatively minor manipulations of the skin temperature information.
So, say you’re under the covers. Your blood temperature is spot on, but your skin is saying it’s a little too warm. You stick a hand or foot out from under the covers, and it starts sending back the message that it’s cool. The hypothalamus looks at a sort of weighted average of this information and says, “It’s just right.” As long as it thinks that, it doesn’t send out any of the hormones that trigger you to do temperature-adjustment stuff, so you stay comfortable.
Still more speculatively: Your feet are probably the part of your body most subject to external temperature variation: they’re farther from your heart and your hypothalamus than anything else, and they’re prone to circulation restrictions, as others in the thread have pointed out. It’s possible that the hypothalamus treats your feet as early warning sensors of a sort, weighting skin temperature data from them more heavily than from parts nearby, like your hands or face. That might mean you could manipulate your temperature perception more easily with your feet than with your hands.