A cooling system for an engine capable of switching between lean combustion in which air-fuel mixture, an air-fuel ratio of which is leaner than a stoichiometric air-fuel ratio, is burned and stoichiometric combustion in which the air-fuel mixture, the air-fuel ratio of which is equal to the stoichiometric air-fuel ratio, is burned, the cooling system comprising: a pump configured to supply an engine coolant; a bore passage through which the engine coolant flows to cool a cylinder bore of the engine; a head passage that is provided to a cylinder head of the engine and through which the engine coolant flows to cool a portion of the cylinder head adjacent to a combustion chamber; a first passage through which the engine coolant flows into the pump through a radiator configured to cool the engine coolant after flowing through the bore passage and flowing through the head passage; a second passage through which the engine coolant flows into the pump by bypassing the radiator after flowing through the bore passage and flowing through the head passage; a first fluid temperature acquisition section that acquires a fluid temperature of the engine coolant discharged from the pump and flowing into an inlet of the bore passage; a second fluid temperature acquisition section that acquires the fluid temperature of the engine coolant flowing through the head passage; a temperature regulator that is arranged in the first passage and opens/closes the first passage, so as to regulate the fluid temperature of the engine coolant flowing through the first passage; a flow rate regulator that is arranged in the second passage and opens/closes the second passage, so as to regulate a flow rate of the engine coolant flowing through the second passage; and a control unit configured to control actuation of the temperature regulator and the flow rate regulator, characterized in that the control unit is configured to, while controlling the actuation of the temperature regulator on the basis of a detection result of the first fluid temperature acquisition section, control the actuation of the flow rate regulator on the basis of a detection result of the second fluid temperature acquisition section. a pump configured to supply an engine coolant; a bore passage through which the engine coolant flows to cool a cylinder bore of the engine; a head passage that is provided to a cylinder head of the engine and through which the engine coolant flows to cool a portion of the cylinder head adjacent to a combustion chamber; a first passage through which the engine coolant flows into the pump through a radiator configured to cool the engine coolant after flowing through the bore passage and flowing through the head passage; a second passage through which the engine coolant flows into the pump by bypassing the radiator after flowing through the bore passage and flowing through the head passage; a first fluid temperature acquisition section that acquires a fluid temperature of the engine coolant discharged from the pump and flowing into an inlet of the bore passage; a second fluid temperature acquisition section that acquires the fluid temperature of the engine coolant flowing through the head passage; a temperature regulator that is arranged in the first passage and opens/closes the first passage, so as to regulate the fluid temperature of the engine coolant flowing through the first passage; a flow rate regulator that is arranged in the second passage and opens/closes the second passage, so as to regulate a flow rate of the engine coolant flowing through the second passage; and a control unit configured to control actuation of the temperature regulator and the flow rate regulator, characterized in that the control unit is configured to, while controlling the actuation of the temperature regulator on the basis of a detection result of the first fluid temperature acquisition section, control the actuation of the flow rate regulator on the basis of a detection result of the second fluid temperature acquisition section.