A cooling apparatus for a marine propulsion system outdrive unit that can be attached to an outdrive unit without the need to drill holes in any portion of the outdrive unit. The cooling apparatus has a distribution tube assembly with at least one pickup port and a water delivery feature such as dump ports, the pickup port being open to receive cooling water into the distribution tube assembly when mounted on a marine propulsion system outdrive unit and the water delivery feature positioned to face the drive unit for delivering cooling water from the distribution tube assembly to the outdrive unit. A no drill bracket attached to the distribution tube assembly attaches to the lift ram assembly shaft of the outdrive unit, and an upper mounting bracket that is attached to the distribution tube assembly attaches to the outdrive unit.