An auxiliary power unit for an aircraft, including an internal combustion engine having a liquid coolant system, a generator drivingly engaged to the internal combustion engine and having a liquid coolant system distinct from the liquid coolant system of the internal combustion engine, a first heat exchanger in fluid communication with the liquid coolant system of the internal combustion engine, a second heat exchanger in fluid communication with the liquid coolant system of the generator, an exhaust duct in fluid communication with air passages of the heat exchangers, and a fan received in the exhaust duct and rotatable by the internal combustion engine for driving a cooling air flow through the air passages. The liquid coolant system of the engine may be distinct from fuel and lubricating systems of the auxiliary power unit. A method of cooling a generator and an internal combustion engine is also discussed.