In the present invention, a cooling system for an internal combustion engine is provided with a flow path switching valve that, from among a plurality of cooling water passages, sequentially switches at least one cooling water passage that distributes cooling water. When a control device for the cooling system controls the flow path switching valve and switches the cooling water passage in accordance with the warm-up state of the internal combustion engine, the control device suppresses the amount of cooling water that is newly distributed to the cooling water passage.