A cooling apparatus of an engine of the invention has a circulation passage for supplying cooling water to head and block passages through a heat exchanger. The apparatus circulates the cooling water through the circulation passage when a second condition is satisfied and then, a first condition is satisfied. The first condition includes a water supply condition that a supply of the cooling water to the exchanger is requested. The second condition includes the water supply condition and a condition that a cooling water temperature is lower than an engine completely-warmed water temperature.