My grandma has a 2004 aztek and the heat went out. Will
replacing the water pump fix this problem?
If the WP was the problem it will fix it. Be sure and purge air out of the system after replacing the pump.
Run the car with the radiator cap off until the thermostat opens. Watch the coolant flow in the radiator neck. If the water pump has failed, you will not see any coolant flowing past the radiator neck. It could also be a stuck thermostat so if the coolant never flows, I would check/replace the thermostat first and then move on to a failed WP diagnosis. Also make sure the coolant is at the correct fill level.