A cooling system for a marine vessel is configured to allow all cooling water to flow out of the cooling circuit naturally and under the influence of gravity when the marine vessel is removed from the body of water. All conduits of the cooling circuit are sloped downwardly and rearwardly from within the marine vessel to an opening through its transom. Traps are avoided so that residual water is not retained within locations of the cooling system after the natural draining process is complete. The opening through the transom of the marine vessel is at or below all conduits of the cooling system in order to facilitate the natural draining of the cooling system under the influence of gravity and without the need for operator intervention.