250hp 2006 evinrude etech overheating problem

The engine will shut down when going over 10 mph. Changed the water pump but it still runs hot when tested. Can anyone explain how the water circulates in the engine. I checked and the water is not getting up on the top of the engine block when I took the two plugs out where the thermostats are located. I connected a hose to the pipe supplying the water from the water pump and it does runs up to the thermostats. Can it be still a problem with the water pump not pushing the water up in the engine? Water does comes out through the spitting plug.