metals, sure. The problem with plastics is that plastic is not plastic, it's a plethora of different chemical structures. Very difficult to recycle some of them, even if sorted.
As long as the temperature inside remains constant, as much cold leaks out as is transported inside. So the only residual heating outside would be from inefficiensies in the system, not the moving process itself.
You stated that you cant connect a car battery to a fridge. You said nothing in your comment about 12v. I can connect my car battery to my fridge no problem.
They do discuss it briefly in No such thing as a fish ep. 43.