A body at rest in a gravitational field ((as standing on the surface of the earth) is the same as a body being accelerated. A free falling object is equivalent to not accelerating (The equivalency principal). The Accelerated one at rest would heat up.
OK so maybe I didn't articulate that so well please let me try again. The equivalence principle states that gravitational and inertial forces are similar in nature and often indistinguishable. I was attempting to agree with the answers above that a body at rest in a gravitational field will heat up. My point was that of course it with heat up because a body at rest in a gravitational field is equivalent to a body being accelerated as with the man in the elevator being accelerating upward. And of course Accelerated bodies heat up.