A cooling apparatus has a heat exchanger for performing heat exchange between cooling water and fluid, and a flow rate regulator valve for regulating a flow rate of either the cooling water or the fluid which pass through the heat exchanger. A cooling temperature of the fluid is preset. A temperature of the cooled fluid is detected, and an opening degree of the flow rate regulator valve is changed when there is a difference between the detected temperature and the preset temperature. Simultaneously, either a temperature difference of the cooling water and the fluid or a flow rate of the cooling water is detected. The opening degree of the flow rate regulator valve is corrected or compensated on the basis of a result of the detection, thus enabling suitable temperature control of the fluid in accordance with a variation of the temperature or flow rate of the cooling water.