A rotary engine has a substantially trochoidal-shaped housing cavity in which a rotor planetates. A cooling system for the engine directs coolant along a single series path consisting of series connected groups of passages. Coolant enters near the intake port, passes downwardly and axially through the cooler regions of the engine, then passes upwardly and axially through the hotter regions. By first flowing through the coolest regions, coolant pressure is reduced, thus reducing the saturation temperature of the coolant and thereby enhancing the nucleate boiling heat transfer mechanism which predominates in the high heat flux region of the engine during high power level operation