First things first. This was done on a 1980 733i, which means it's not 100% the same as the 1982 and newer cars. However, most of it will still apply. Also, it worked for me but that doesn't mean it will work for you. I TAKE NO RESPONSIBILITY IF IT DOESN'T WORK FOR YOU, OR IF ANYTHING BREAKS, YOUR WIFE OR HUSBAND LEAVES YOU AFTER DISCOVERING YOUR NEW VOCABULARY DURING THIS PROCESS, OR ANY OTHER REASON. You can however e-mail me with any questions at firstname.lastname@example.org and I will answer as best and as quickly as I can. I'll also try to post items others discover doing this to help people with other cars newer than mine.
And remember, after doing a heater core, HVAC vacuum issues seem soooo easy to fix.. :)
I did this the first time in about 5 hours total working time. I found that it wasn't so much a matter of being a midget or contortionist, but rather having a good chiropractor since a good deal of the time you're laying across the parking brake lever.
I wish I had a digital camera for this, so I could also post a series of pictures to help along, but alas, I did not. I will try to describe things as completely as possible for everybody to follow along.
The steps are in the order I did them, and some can be done in a different order if desired.
I did this with the tools in the trunk, plus the following: socket wrench with long extension with 8mm and 13mm sockets and a small tip standard screwdriver.
Remove the center console controls. Here you want to remove EVERYTHING below the center dash vents. This includes the radio, HVAC controls, OBC if you have it (or clock on the older ones). You'll start by removing the radio. In the bottom of the spot for the radio you'll find two bolts holding the bottom of the HVAC control panel in place. In the top of the HVAC control panel you'll find another four small screws holding in the top. This will allow you to start removing the panel. Once you have it slid out far enough to get to the connections, start unplugging them. DISCLAIMER: I would make each connection so you know where it goes back to. I personally don't do this, it's a knack I have, but if you don't and can't remember where things go, it's not my fault. On my car I have a cable controlled temp control. I removed the lever from the wheel to allow the panel to come out without having to either unhook the cable from the lower lever or have the switch dangling in front of where I need to get into. This is also a really good time to replace all the bulbs for lighting the panel, since you have to tear into this the same way to replace them.
Remove the ashtray, and the rear socket for it. This is held by four screws in the corners. Probably not really necessary to do, but gave me a place to grab the front to wiggle it out of place and out.
Start removing the center console from the rear forward. Start by removing the screws the hold the rear seat vent panel in place. WOrk your way forward to the front section of the center console. On my car, being a 1980 model, I have my window switches in the rear section. Unplug the connectors for any electrics that are in this section (power seats on newer models, etc.).
Remove the front section of the center console. You'll need to remove the shift handle (this is where the small tipped screwdriver came into play) to slide the console up over it. You'll want to drop the lever back into first, so make sure the car is stable and not going to roll (you'll have the parking brake off now as well unless your back is FAR more flexible than mine). On mine this was held by a nut on the rear of the front section, and two screws, one on each side, on the front sides by the floor vents. Once this is off you will also need to remove the ducting from the heater box to the rear section. This would be easier if I removed the bottom portion of the rear section completely, but I just removed the molded tube assembly itself and left the lower rear section in place since I can be lazy.
Step 5, the fun begins:
Remove the cover over the vacuum solenoids (behind where the ashtray was). Also unbolt the solenoid assembly from the heater box. This is when you find why it's necessary to remove the radio and everything above, it gives you a nice place to shove all the wires, vacuum parts, etc. into without having to disconnect everything. I slid the solenoid assembly up behind the cross member into the top section to get it out of the way. Be careful with the vacuum lines unless they're fairly new!
At this point, you should have fairly clear access to the rear of the heater box. Behind the plastic box cover is the heater core. You will need to unbolt the vertical dash strut (two bolts) from the center tunnel now. CAREFULLY pry it slightly towards you and to the left (left hand drive cars, don't know about right hand drive, but guessing it's the reverse of this). You just need enough room to get to the small screw in the bottom left corner of the heater box cover with the socket wrench. I only had to move mine approximately a half inch to the side and about the same towards me. Unclip and move any wires in the way.
Start by removing the two screws on the bottom corners. There are four clips that hold the cover on at this point. Be careful when removing them so you don't lose them, they're spring steel and WILL fly into nowhere-land if you're not careful If there's anything else attached to this cover that I forgot about, remove them as well. Now the cover should be loose.
With the vertical strut there, there's not a lot of room to get this cover out. However, I found that with a fair bit of careful wiggling, and creative use of four letter words, I slid it out to the right of the strut and forward and out. You will probably also have to disconnect the vacuum hose coming gout of the cover from the solenoid assembly. You should now see your heater core in plain view.
Now you get to go up front and remove the cowling. Remove the grills over the cowling cover (this is easier with the wiper arms removed, but you can get it off carefully without removing the arms). Undo the screws holding it down on the top (4 on mine) and along the front edge in the engine compartment (also 4 on mine, but should be 8 :) CAREFULLY lift the cowling cover up, making sure not to damage your flap servos or flaps (or if they're in pieces like mine, just yank it up). Also easier to do with the wiper arms removed, but I did it with them in place. You'll now see the hoses for the heater core. Undo the clamps and pull the hoses off (careful about spilling the antifreeze, which you will do :) My core was empty of fluid, but if there's still fluid in the core you can stick a tube on a syphon down one of the tubes to pull as much fluid out as you can. Make sure that you move the tubes out of the way so they don't interfere with the tubes when they go back in. Also, don't cut your finger on the splash shields, they pop right out and give you a lot more room (and now you know this BEFORE getting to the reassembly part, ugh...)
Go back inside the car, and carefully pull the heater core towards you until it hits the vertical support. Undo the tube on the side opposite the support and pull it from the heater core. Push the tube back up into place to get it out of the way (or out if you can, as you prefer). You should now have the heater core with just the left tube attached. Push it back forward, nd start the careful process of slicing your fingers up on it wiggling it around to get it past the strut. It's a VERY tight squeeze, but I did get it out without damaging the tube or core.
Step 11 IMPORTANT!:
Examine the core. If it is like mine, it will appear that it was just the o-rings that went bad and caused this whole mess. If so, option A. Have it tested and if good, you have an e-Bay item to sell. Or you can do option B. Take the dead, or no longer wanted core, and carefully stop and smash it as best you can. This step is VERY important as it releases much of the stress that has built up trying to get the thing out. I don't recommend dynamite. However, depending on stress levels, it might be the only way. This is also a good time to clean the heater box out of any remaining antifreeze, dirt, small rodents or illegal immigrants.
Prep the new heater core for installation. This included mounting BOTH tubes (tighten the left tube completely, but leave the right loose, it's coming back off), wrapping the self stick (especially where it's not supposed to stick but will anyway) foam around the core. The two triangular(ish) pieces go on the back of the core on the plastic side pieces (at least that's where mine were on the old one, so the new went there as well and seemed to fit properly). The other foam pieces go on the tubes to cushion them against things you can't see way up in the dash. Match locations of the original foam (there should be marks on the tube from where it's been sitting for the last 20 years). Now, pull the foam away from the mounting point on the right tube and remove the tube.
Now it's time to get the new core back in. Start by putting the right tube through and out the cowling (as if it was on the core). Take the new core and wiggle it back into place, doing the reverse of how it came out (you did pay attention, didn't you?). Be VERY CAREFUL NOT TO BEND THE TUBE! It takes a good deal of patience here to get it in without damaging anything. Don't push it all the way in the box yet. Carefully attach the right tube to the core, once again being careful not to bend either tube. Make sure the bolts are snug, and carefully push the core back into place. Make sure the foam stays flat against the core and doesn't peel off. Swearing at it doesn't help, I tried.
Once the core is in place, go back to the cowling and check the gaskets for the tubes are still in their proper place, Repeat if needed to get the gaskets in place (good to do this now rather than after everything is back together, it's a pain otherwise (don't ask...).
Replace the cover on the box., making sure there's nothing trapped inside (like two paper towels used for cleaning the box out with just a bit sticking out to notice at the last second). Be careful not to pinch any wires or vacuum hoses behind the cover (they stayed out of the way nicely till now, and they will all fall in-between the cover and box repeatedly at this point). Hook the spring clips back on the back and snap over the front, and replace the two bottom screws. Reattach the vertical support with the two bolts now.
Go back to the cowling and attach the heater hoses to the tubes. Replace the splash shields that you didn't just now discover come out really easily :)
At this point, I reconnected all the electrics and started the car so I could check for leaks and electrical function before everything was completely back together. Finding no leaks and everything still working, I started reassembly with the HVAC control panel. and got it back into place (replacing bulbs, etc.) Make sure you don't pinch any wires, or forget to connect any of the connectors you unplugged.
Step 18 (yada, yada, yada...):
Reverse the disassembly process so that you appear to have a center console again, and enjoy the heat!