Heater core

No. Too much pressure could be from a bad radiator cap. Normal operating pressure is around 14psi.

I have replace cap but still does the same thing

Have you tried a flush and fill with a new thermostat?

Why do you think there is too much pressure?

I tested thermostat thermostat is good and why I think it's got too much pressure is you can't squeeze the top radiator hose once it has been running after thermostat opens up

My crown Vic has a heater core but the previous owner by passed a hose into the motor is that bad I need answer because my crown Vic still leaks water