An aircraft propulsion system and method of cooling the same are provided. The system includes a hydraulic pump, an intermittent IC engine, a hydraulic motor, an engine oil pump, and a cooling system. The intermittent IC engine drives the hydraulic pump. The hydraulic motor is powered by the hydraulic pump and drives a propulsor fan. The cooling system includes a first heat exchanger (AIR-EO HEX) and a second heat exchanger (EO-HF HEX). The AIR-EO HEX transfers heat between flows of engine oil and ambient air. The EO-HF HEX transfers heat between flows of engine oil and hydraulic fluid. The hydraulic pump provides motive force to cause the hydraulic oil to pass through the EO-HF HEX and back to the at least one hydraulic pump. The engine oil pump provides motive force to pass the engine oil to and through the AIR-EO HEX, the EO-HF HEX, and the intermittent IC engine.