PURPOSE: To eliminate excessive cooling and insufficient cooling throughout a cooling system, by selectively communicating water passages for preheating an intake-pipe, and a heater with the head side or crank casing side of the engine in accordance with the temperature of cooling water.

CONSTITUTION: When the temperature of cooling water is low upon starting of the engine, the output of a comparator is L level so that selector valves 8, 16, 22, 26, 32 are deenerigized to communicate a water passage 4 with a bypass water passage 9, and therefore, cooling water is passed by a radiator 5 to circulate between the engine and the crank casing 1. Further, the selector valves 16, 22, 26, 32 communicates water passages 28, 21, 25 and 31 with passages 17, 23, 28 and 34, respectively, so that cooling water is passed by a radiator 13 and circulates between the head 2 and the bypass water passage 17 through an intake-air pipe preheating water passage 24 and a heater 30. The outlet temperature of cooling water exceeds T, the output of the comparator becomes H level so that the cooling water circulates between the crank casing 1 and the bypass water passage 9, and further when the outlet temperature of cooling water exceeds TH, the output of the comparator becomes H level so that cooling water flows by way of the radiator 5.