I doubt that the heater core is the problem. If the heater was working before the water pump was replaced I suspect that something is not properly connected, such as the vacuum line for the heater controls.
The vacuum line for the heater controls may have been pulled loose while changing the water pump. Try changing the settings on the A/C controls and see if the air shifts from the dash vents to the floor vents to the defroster vents. If changing the control from heat to vent to defrost makes no change in which vents the air is coming out of the vacuum line is disconnected.
If that is not it then:
According to the FSM for a 2004:
Both of the heater hoses should be HOT to the touch (coolant return hose should be slightly cooler than the supply hose. If the coolant return hose is much cooler than the supply hose, locate and repair the engine coolant flow obstruction in the heater system.
If both heater hoses are cool to the touch, inspect the engine cooling system.
OBSTRUCTED COOLANT FLOW Possible locations or causes of obstructed coolant flow are as follows:
Pinched or kinked heater hoses.
Improper heater hose routing.
Plugged heater hoses or supply and return ports at the cooling system connections.
Plugged heater core.
If proper coolant flow through the cooling system is verified, and heater outlet air temperature is insufficient, a mechanical problem may exist.
MECHANICAL PROBLEMS Possible causes of insufficient heat due to mechanical problems are as follows:
Obstructed cowl air intake.
Obstructed heater system outlets.
Blend-air door not functioning properly.
If the heater outlet air temperature cannot be adjusted with the temperature control knob on the A/C-heater control panel, the following could require service:
Blend-air door binding.
Faulty blend-air door motor.
Faulty A/C-heater control.
Faulty related wiring harness or connectors.
Improper engine coolant temperature.
You did not use Barsleak or some other radiator additive did you? I have seen some of that stuff that stops up heater cores.
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