It's good that these things...
It's good that these things are hidden under the dash where no one can see them. More of you than not will have a heat-only box so yours might be simpler and lighter, but the procedures that apply will be the same for both. If you are pulling yours out of a car with an intact interior, it would be wise to pull the front seat and also protect your carpet from dripping antifreeze.
Have you ever noticed that there are some aspects of a musclecar restoration that are not very glamorous? I'm not talking about getting dirty rebuilding your engine or being coated in dust as you prep your car for paint. There are rewards for successfully completing those jobs. A well-detailed, strong engine or flawless, baby-butt smooth paint will bring you a lot of praise for your efforts.
But when was the last time you heard anyone remark about how great someone's heater box looks . . . probably never. But I'll bet you appreciate a properly working A/C on those mid-summer afternoons, or a little heat on a late-season, early morning cruise. If nothing else, you'd simply like your heater core to not drip antifreeze on your fresh carpet. No, it's not a glamorous job, but it's oh so much easier (read actually possible) if you take the time to pull the whole assembly out of the car.
This heater/air-conditioning box is out of a '68 Barracuda and is part of our progressive restoration series. The guys at Muscle Car Restorations (MCR) have done a lot of these over the years and have few tips that will save you some time and frustration.

The heater-core cover fiberglass...

The heater-core cover fiberglass gets brittle with age; if you just slip a screwdriver behind the clip to pry if off, you'll break the little ridge that holds the clip in place. Instead, use the screwdriver as shown to pry down and lift the edge of the clip up and then out.

The hoses are color coded...

The hoses are color coded so take careful notes on the routing. The same goes for the wiring. Taking detailed photos is a really good idea. You'll need to test the vacuum actuators and make sure they work in both directions-they should push and pull. New ones are not available so you'll have to track down good used ones if any of yours are bad.

Don't be surprised to find...

Don't be surprised to find broken fiberglass, especially around the support rod that attaches to the cowl vent opening. MCR uses a two-part bumper repair product: Fusor 142 Extreme Bumper Repair Adhesive from the Lord Corporation. It's strong, flexible, and sandable. Don't be afraid to be generous with the adhesive; this repair doesn't need to be pretty because it's hidden inside the box.

With the cover off, you can...

With the cover off, you can remove the screws that retain the heater core.

Here is a part that has been...

Here is a part that has been recently replaced. This is the blower speed resistor. The resistor coils protrude into the airflow and are somewhat exposed to the climate. It's common for them to get rusty and break off.

You wouldn't be the first...

You wouldn't be the first one to try to remove the blower motor by removing the three nuts on top of the housing. Instead, remove the three 1/4-inch screws from around the perimeter and then carefully pry the motor with the attached cage off the lip. Test the motor by simply applying power to the leads. Listen and check for bad bearings.

The yellow fiberglass insulation...

The yellow fiberglass insulation firewall pads are usually bad, and repops are not available for A/C cars. You can make one out of a non-A/C car pad or cut one from a piece of a fiberglass hood blanket that you can find under a number of car hoods. A piece of sound deadening pad from under your car's carpet could also work well.

This is the evaporator temperature...

This is the evaporator temperature control switch. It has a long probe attached to it that monitors the temperature inside the evaporator coil and will shut the system off if it starts to freeze up. The probe can be difficult to remove, but it must come out to remove the coil. Don't be afraid to pull hard.

Removing the evaporator-coil...

Removing the evaporator-coil cover reveals a fairly fine screen positioned over the coil. Remove the screen to get at the coil itself. Unless it's severely damaged, just clean and reuse it.

This is why you need to remove...

This is why you need to remove the coil. Most have never been removed, and this one has forty years of debris behind it. If your A/C system worked fine before you took it apart, then all you should need to do to your coil is clean it and comb some of the fins. If you don't know for sure that your coil is good, it would be wise to take it to an A/C shop to have it tested for leaks. In this case, they are not available new.

The foam on the vent doors...

The foam on the vent doors is always bad, and again, new parts are not available, but fortunately, the foam from a fuel tank pad works great.

YearOne does supply these...

YearOne does supply these firewall gaskets so be sure to make use of those as well as the foam tubes around the heater core pipes. The firewall insulation pad was actually in pretty good shape so it was reused.

This end of the box receives...

This end of the box receives fresh air from an opening on the bottom of the passenger side of the cowl. The foam gasket is commonly bad, but a roll of 3/4-inch foam tape from a local hardware store works great. The small rod hooks to the bottom of the cowl to draw the box up tight.

Use more foam tape (about...

Use more foam tape (about 1x1-inch) to seal the blower motor and cage assembly to the airbox.

The foam around the A/C opening...

The foam around the A/C opening that seals to the back of the dash is not available (that we are aware of), but it is often OK to reuse it. Just wash it in some soapy water and maybe flip it over. If yours is really bad, any soft foam that you can get at a hardware or craft store that you can cut or glue to fit will be fine.

it's a good idea to get a...

it's a good idea to get a buddy to help you reinstall the entire assembly. What you need is someone on the firewall side to thread the nuts on the studs that hold the unit to the firewall.

Before you tighten up the...

Before you tighten up the firewall nuts, insert this rod through the vent opening, hook it into the cowl, and insert and tighten up the bolt to seal the box against the bottom of the cowl.

Don't be tempted to skip installing...

Don't be tempted to skip installing the foam around these tubes because it keeps debris, water, and cold air out of the interior.

As you can see, we still have...

As you can see, we still have a lot of work to do to finish our Barracuda, but this gets us one step closer.