There are fallacies to the above argument. Most heat energy emitted by the engine is in the invisible infrared portion of the spectrum. What appears to us as black, white, red, or green in the visible spectrum is not what we would see in the infrared spectrum. Painting an engine increases radiant cooling but the color of the paint doesn't. The second fallacy is that you also have to ask what happens to the radiant energy being emitted by the engine.
Black paint has high absorbency and high emittance.
Better would be white paint that has low absorbency and high emittance. An engine contained within a bare aluminum cowling should be painted white not black to reflect the radiant energy back to the cowling. Another technique would be to paint the inside of the cowling black to eliminate reflection of heat energy. If the aircraft had a plastic cowling then the engine need not be painted white because of the low reflectance of plastic. Most heat from the engine is transferred to the atmosphere by convection rather than by radiation.