If the object is at rest it would imply that gravity transfer heat without an increase in potential energy, and there are no other forces that produce work. This would violate the conservation of energy.

If the object is at rest it would imply that gravity transfer heat without an increase in potential energy, and there are no other forces that produce work. This would violate the conservation of energy.

Regarding your comment "any contact forces imposed on an object will increase that object's heat energy": this is incorrect, friction only results in heat exchange when there is relative motion between the surfaces, not when they are at rest relative to each other.