If you don't have a thermostat in the system, it should not have any effect on the water flow. You might try attaching a hose the the water tube that goes up to the block and make sure the flow through the system is good. Sometimes a defective head gasket will allow compression into the cooling system and overpower the pump pressure causing the engine to overheat.
Lack of a thermostat may not affect water flow, but lack of the plastic thermostat HOUSING and check valve certainly will. Those parts must be in there or the pump will suck exhaust down through the return water tube, effectivly admitting air into the pump inlet. They are good water pumps, but lousy air pumps.
So...are the housing and check valve parts in the head?