The resistor itself is on the expensive side (in the region of 50EUR, as I recall), but thats still nowhere near the amount of hours you'd pay for, if you delivered the car to a dealer to have this fixed .-)
Thank you very much for this (old post) advice. My aged J63 developed the same problem, with the same cause.
Lennart is right that the fan motor and resistor are horrible to get at, and that the wiper mechanism has to be removed before the heater box. On mine, right-hand-drive, one of the heater box fixings is incredibly difficult to get at. I had to buy a 10 mm flexible-end ratchet spanner, and extend it with another spanner, to reach past the heater box, heater and air-con pipes, and brake master cylinder, and even then it must thave taken 15 minutes to remove that single nut.
The good news is that a new resistor pack is not needed. There's a little thermal fuse, cost 99p online (about €1.20) including postage, along the side of the resistor. Cut out the old fuse and connect a new one, with a crimp or screw connector rather than solder, and save the cost and waste of a complete resistor. The critical information needed is the cut-out temperature, which is 240 C for mine. Look for "thermal fuse 240C" and buy one before starting work. Check the temperature marking on the old fuse when you do get it out, though: this is a safety-critical part, to avoid a fire if the heater air-flow stops.
The reason my resistor overheated is that the fan motor bearings needed lubrication, so the fans were not running fast enough. I've given the bearings a few drops of oil (transmission oil, but I don't think that's critical). Ideally I would have replaced the fan motor's carbon brushes as well, but they look to have another 100 000 km before wearing out.
Before fixing the heater airbox back in the car, rest it on top of the engine and connect up all 3 cables, turn on the ignition and test the fan at all speeds. That can save a lot of work if something's not running smoothly and quietly.
I would like to replace the sound-insulating soft cover of my heater air-box, because after 24 years it's getting ragged. Is it possible to get the right sort of engine-compartment-grade fabric and make up a new cover?