1. Breaking the second law of thermodynamics (or even better, the first one). Breaking laws of physics has to be somewhere in someone's famous last words, I'm sure...
Making heat flow from cold to hot is pretty simple on a scale large enough where you can moving something at a measurable fraction of the speed of light.
Imagine a giant turbine where the blades move out of the way as fast as light advances down the throat, so photons moving through the turbine never collide with a wall. Then make the backsides of the turbine blades retroreflectors (or stepped flat mirrors like stair steps) so light coming from the other direction, trying to go backwards through the turbine, is reflected back to the source. Then you have a broad-spectrum one-way light path. If you put it between two objects, the infrared energy will always flow in the same direction, regardless of relative temperatures.
Unfortunately the turbine needs to have a huge radius or such a turbine would fly apart, since the blades do need to move at a small measurable fraction of the speed of light.
But there you go. I've come up with a way to save the entire universe, and am just awaiting my royalty checks from advanced alien civilizations.