PROBLEM TO BE SOLVED: To provide a cooling device of an engine capable of enhancing warming-up efficiency of the engine.SOLUTION: In a cooling device of an engine, engine cooling water 15 in an in-head cooling water jacket 12 is circulated into a cooling water pump 3 through a bypass passage 4 bypassing a radiator 18, and the engine cooling water 15 in the in-head cooling water jacket 12 is circulated into the cooling water pump 3 through the radiator 18 by a thermostat 1 when a water temperature of the engine cooling water 15 detected by the thermostat 1 exceeds a prescribed value. An engine cooling fan 13 is arranged in a front side of the engine, engine cooling air 13a is blown backward from the engine cooling fan 13, and the thermostat 1 is stored in a thermostat chamber 8 provided in a rear portion of the cylinder head 5.SELECTED DRAWING: Figure 1