A cooling system of an internal combustion engine includes a flow channel switching valve for sequentially switching between a plurality of cooling water passages so as to distribute cooling water to at least one cooling water passage. When a control device for the cooling system switches between the cooling water passages by controlling the flow channel switching valve in accordance with the progress of warm-up of the internal combustion engine, the control device suppresses the distribution rate of the cooling water to the cooling water passage to which the distribution of the cooling water is just started.