It comes out from the inside.
This is one of the most complicated 'under-dash' projects you'll ever undertake! See "Related Questions" below for more background, information and helpful tips.
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I believe the procedures are either covered, or linked to the "Related Question" below regarding replacing the heater core - which is deep down inside the dash.
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It is on the centre side of heater against the firewall inside cabin. You must disconnect steering column and remove the entire instrument console and angle it out on the passenger side. Easier than it sounds. Look for video by 'Makuloco' on youtube
After you remove the hoses from the core, remove the nuts and bolts that secure the heater case to the firewall in the engine bay. Inside the cab you will have to remove the glove box assembly for clearance. then disconnect the blower fan wiring. there may be another bolt securing the heater case to the firewall on the inside of the cab. Then you should be able to remove the heater case. You'll have to split the heater case to get to the core.
Remove the center switch console. remove the 4 spring clips holding the square heater motor housing and remove the housing. Inside the heater motor housing Remove the two spring clips holding the heater motor in Remove wiring connections and then remove the heater motor. Install new heater motor and installation is in the reverse order of above.
Remove the center console remove the floor vent remove the heater core cover the heater core is right under the climate control unit remove the two screws that hold the heater core in place, open the hood and remove the heater hose from the heater core lines, now go inside and pull out the old heater core you don't have to remove the whole dash just the front of it
Chilton's says to remove hoses from the 2 connectors inside engine compartment and remove the dash panel and lower panel. Then reach inside and pull the heater core out.
You have to remove the entire dashboard to expose the heater box. Then you can disassemble the heater box. This is a HUGE job. I've done it several times and it's every bit of 2 days for a do it yourselfer.
The AC has to be dischared, and the AC lines have to be removed at the firewall. The AC drier has to be remved, because there are nuts on the outside of the firewall under the hood to remove that are hidden by the drier. I believe there are 4 nuts to remove, but there might only be three.
remove the four nuts in the engine bay on the heater box near where the heater core hoses enter. Drain coolant remove the hoses and pull the heater box out from the inside of the car. Remove clips holding heater core, than put your new one in.
Remove the hoses going to the heater core. Use a regular water hose with a high pressure nozzle and flush both ways.