A passive cooling system for an auxiliary power unit (APU) installation on an aircraft is provided. The system is for an auxiliary power unit having at least a compressor portion of a gas turbine engine and an oil cooler contained separately within a nacelle. The system includes the auxiliary power unit housed within the nacelle of the aircraft, an engine exhaust opening defined in the aft portion of the nacelle and communicating with the gas turbine engine, at least a first air inlet duct communicating with a second opening defined in said nacelle and with said compressor portion and the oil cooler is located within a second duct communicating with an opening other than the engine exhaust opening of said nacelle and with the engine exhaust opening. Exterior cooling air and engine exhaust ejected through said engine exhaust opening entrain cooling air through said second duct to said oil cooler, and thus provide engine oil cooling. An exhaust eductor is also provided.