I am trying to find a solution for a specific subset of the Stealth in Space Problem: dealing with waste heat without tipping off properly positioned observers. This question is scoped specifically this one way of tackling the problem, not to the problem's other aspects (such as trapping said waste heat). I'm open to bending the laws of nature, but I would rather do this in a knowing and consistent way, and understand the possible unintended consequences, and at least the orders of magnitude of things like efficiency and energy levels involved, thus the science-based tag.
My goal is to come up with a paradigm-shifting radiator/heatsink-like technology that is good enough to deal with the waste heat a spaceship may produce as a result of her activities (preferably good enough to deal with a reactor running strongly enough for life support and other typical on-board equipment), but that cannot be used in a way that completely invalidates other power plants (e.g. running a Stirling engine on waste heat of life activities alone).
Here is my starting point, which is open to adjustments:
Let's postulate a technology that allows building radiators that radiate into a direction that is perpendicular to all three of our spatial dimensions - a 4D radiator. For every X³ of volume of the device, it can radiate as well as a normal modern radiator with an X² surface; the device has a density of approximately 1/5 of a kg per litre; cost is yet undecided. The background temperature of the fourth-dimensional void is close to 3K. For now, assume there are no ways for other ships to remotely perceive what's going on the fourth dimension near the stealthy ships, and thus no way to trace that irradiated heat.
Is the above setup already good enough for my goals? Or would it require some adjustments (e.g. scale radiative capability to a different power of X, perhaps)? Or is my request such that satisfying the stealth usage requirement will under all circumstances result in 4D Stirlings so good that they replace all other engines?