Dad - I think if your heater is blowing lukewarm either you need to up the thermostat [running the engine too cool], or you've got a partly blocked heater core - the heater should be getting a good flow of water the same temp as what's pushing against the thermostat, tho' you could have the hose connections to the wrong place on the engine
not clear on how it can be hooked up "backwards", one hose goes to the water pump, which is drawing water from the bottom of the rad, and will also draw water from the heater, other hose is from the block on the hot side of the thermostat, pushed by the pump ... water can only flow thru the heater from the upper "hot" location back to the pump, and the direction thru the heater core doesn't matter
Bill