Are you sure it is the heater core? Do you have overheating and coolant losses issues? A bad heater core would result in that.
It could just be a clogged drain hose from the A/C cooling coil.
HEATER CORE (below center of dash)
CAUTION: DO NOT apply excessive force to heater core pipes.
Removal & Installation
1. Disconnect negative battery cable. Drain cooling system. Raise and support vehicle. Remove drain tube. Disconnect heater hoses from heater core. Lower vehicle.
2. Remove left and right sound insulators from below instrument panel. Remove steering column opening filler. Remove floor outlet duct. Remove heater core cover and heater core. See Fig. 10. To install, reverse removal procedure. Fill cooling system.