An engine cooling apparatus comprising: an engine cooling water path for circulating cooling water for cooling an engine through the engine, wherein the engine cooling water path comprises a water jacket provided inside a cylinder block and a cylinder head of the engine, and an external path arranged outside the engine to enable the cooling water to be discharged from an outlet of the engine with respect to the water jacket and directly returned to an inlet of engine with respect to the water jacket; a heater core cooling water path for circulating the cooling water between the engine and a heater core; a radiator cooling water path for circulating the cooling water between the engine and a radiator; a switching valve for switching a flow of the cooling water such that in a state in which an opening degree of a valve element of the switching valve is 0°, the cooling water for the engine flows through the engine cooling water path, while being prevented from flowing through either of the heater core cooling water path and the radiator cooling water path; a temperature sensor provided in the external path of the engine cooling water path at a position on a side of the outlet of the engine and configured to detect a temperature of the cooling water; switching control means operable, when the temperature of the cooling water is equal to or less than a first setup value, to control the switching valve to switch the flow of the cooling water to the engine cooling water path, and, when the temperature of the cooling water is greater than the first setup value, to control the switching valve to switch the flow of the cooling water to the engine cooling water path and the heater core cooling water path; and exhaust valve area temperature detection means operable to detect or estimate a temperature of an exhaust valve area around an exhaust valve of the engine, characterized in that the switching control means is operable, when the temperature of the exhaust valve area detected by the exhaust valve area temperature detection means is greater than a given temperature, in a state in which the switching valve is switched to the engine cooling water path, to control the switching valve to switch the flow of the cooling water to the engine cooling water path and the heater core cooling water path. an engine cooling water path for circulating cooling water for cooling an engine through the engine, wherein the engine cooling water path comprises a water jacket provided inside a cylinder block and a cylinder head of the engine, and an external path arranged outside the engine to enable the cooling water to be discharged from an outlet of the engine with respect to the water jacket and directly returned to an inlet of engine with respect to the water jacket; a heater core cooling water path for circulating the cooling water between the engine and a heater core; a radiator cooling water path for circulating the cooling water between the engine and a radiator; a switching valve for switching a flow of the cooling water such that in a state in which an opening degree of a valve element of the switching valve is 0°, the cooling water for the engine flows through the engine cooling water path, while being prevented from flowing through either of the heater core cooling water path and the radiator cooling water path; a temperature sensor provided in the external path of the engine cooling water path at a position on a side of the outlet of the engine and configured to detect a temperature of the cooling water; switching control means operable, when the temperature of the cooling water is equal to or less than a first setup value, to control the switching valve to switch the flow of the cooling water to the engine cooling water path, and, when the temperature of the cooling water is greater than the first setup value, to control the switching valve to switch the flow of the cooling water to the engine cooling water path and the heater core cooling water path; and exhaust valve area temperature detection means operable to detect or estimate a temperature of an exhaust valve area around an exhaust valve of the engine, characterized in that the switching control means is operable, when the temperature of the exhaust valve area detected by the exhaust valve area temperature detection means is greater than a given temperature, in a state in which the switching valve is switched to the engine cooling water path, to control the switching valve to switch the flow of the cooling water to the engine cooling water path and the heater core cooling water path.