You need a better understanding of thermal dynamics. Its not the copper pipe that cools, it is only the heat transfer medium (heat exchanger). Its the surrounding ambient air's ability to absorb and remove the BTUs from the heat exchanger that cools, and the warmer the air, the less BTUs it can remove from the heat exchanger. Plus, you have kinda gone around in circles trying to explain what you want to do. I understand your room is hot, and the inside of the case is hot. So, what you need to do is efficiently put cool air into your case (positive air pressure) and create an optimal situation to transfer heat from the heat exchanger (radiator) without saturating the room with that heat. The best way to do that is to put your radiator in a window so it pulls the cool air from the room through it and vents it outside. To keep the cooling tubes from transferring heat into the room you need to insulate them with a non (heat)conductive material. Copper is very heat conductive. Why a copper pipe does not help to transfer much BTUs has to do with the surface area of copper to air, to remove the BTUs. Thats why someone suggested putting cooling fins on the copper tubing to increase heat transfer. But that heat will just be dumped back into your room.
You could make a case out of cardboard and it will cool just as well as an aluminum case because it is not the case that cools, but the efficiency of air flow through the case that cools.
You could use something like the ducting mentioned above to vent the hot air from the radiator outside.Edited by ericld - 2/17/13 at 1:46pm