Speaking thermodynamically

It is a common conception that the body looses the majority of heat from the top of the head. This idea resurfaces every winter, but I have my doubts. I wonder if that "fact" is merely a thermodynamic coincidence, in that the top of the head is at the top of the body. My point is this: if I were hanging upside down, would I loose the majority of my body heat from the soles of my feet? As a corollary, does wearing a hat actually prevent heat loss, or does it merely lower the escape point, so the majority of my body heat is lost from my face?