Another way to put my question would be: Can a heat engine act as a negative thermal resistance? Though that wording makes me expect the answer is “no”.
Suppose we have:
- a heat source (of constant power and finite heat capacity, e.g. an electronic device in continuous operation),
- a “heat sink” in the colloquial sense (a surface exposed to ambient or forced air),
- a closed-cycle heat engine (e.g. a Stirling engine).
Then assuming suitable mechanical interfaces (e.g. flat plates of a common shape), we can compare two different configurations: one in which the heat source is directly joined to the heat sink (A), and one in which the hot and cold ends of the heat engine are interposed (B).
Is it possible for case B to have a lower temperature of the heat source, assuming suitable (physically realizable) characteristics of the heat engine? If it cannot, can the answer be explained in terms of a simple prohibition based on a physical principle (e.g. some of the laws of thermodynamics)?
The answer initially seemed obvious to me: the heat engine is an obstacle between the source and sink and therefore must present some effective (positive) thermal resistance and thus result in a greater temperature of the source in case B than in case A. Someone else thought that the engine would have a cooling effect since it acts to remove some heat from the overall system (turning it into work). I find this implausible but can't think of how to prove it either way.