How do you change heater core in a 1978 Pontiac Phoenix?

Changing the heater core in the '78 Phoenix is primarily an inside job, meaning your going to be working under the passenger side dash.

First, disconnect the battery, then drain the radiator of all coolant (preferably not onto the ground). Remove both heater hoses at the fire wall and remove the rubber grommet on the firewall at the top hose.

Remove the glove compartment door and the glove box itself.

When you look under the dash you are going to see the big plastic heater case. That entire unit needs to be removed and it contains your heater core. Most of the screws are self evident and not hidden but there are two studs that protrude into the engine compartment that you need to remove from that side. They are located on the firewall behind the right (passenger side) valve cover. Look for two threaded studs with an11mm nut and remove those.

Once the heater case is removed carefully remove the rubber gasket and remove the 7 small screws holding the heater core and it's mount in place.

I left out some of the details that are obvious like disconnecting vacuum lines and such.

A third stud is on the lower right of the heater case inside and has a grounding strap attached to it. The factory manual calls for you to use a 1/4: drill and drill that stud out which is the easiest way, unless you want to remove the right front fender.