A cooling system for a marine propulsion device provides a bypass loop around a cooling pump that allows the flow of cooling water through certain components to be reduced or increased as a function of the temperature of those components while causing a full flow of cooling water to flow through other selected heat emitting devices. Using this configuration of components and bypass conduits, the operating condition of the cooling water pump can be continually monitored, including the condition of its flexible vanes. By observing the effective cooling capacity of the system under conditions with the bypass valve open and closed, the effectiveness of the cooling water pump can be assessed and a suggestion of maintenance can be provided.