The correct answer is D) lube oil system. Heat exchangers are most commonly found in the lube oil system of a small auxiliary diesel engine. This is because the lube oil system requires cooling to maintain proper viscosity and lubrication properties. The heat exchanger helps transfer the heat from the lube oil to a cooling medium, such as seawater or fresh water, to keep the oil at the appropriate temperature. The other answer choices are incorrect because fuel oil, governing, and air starting systems do not typically require heat exchangers for cooling purposes in a small auxiliary diesel engine.