A cooling water control apparatus controls a cooling apparatus having first pipe which circulates cooling water through an engine; second pipe which circulates cooling water not through the engine; a switching valve whose state is changed between opened and closed states; and a supplying mechanism which supplies cooling water, and has a determining device which determines whether there is failure of the switching valve based on difference between first temperature of cooling water in first pipe and second temperature of cooling water in second pipe after the command for changing the state of the switching valve from closed state to opened state is outputted; and a controlling device which controls the supplying mechanism to supply cooling water even after the engine stops, when the engine stops while the determining device determines whether there is failure of the switching valve.