Great info Amanda!
For anyone with an OBDI E36 heater controls are the dial types like above,.. you can REPAIR your resistor pack! The pack has a Thermal Fuse at the very end of it that will blow open if the unit overheats at 240 degrees Celcius (you can see it in Amandas pictures - its the silver thing at the end of the green coated fuses). This is why most of them fail. The fuse is: pat microtemp 4468a ckacn 240 degree celcius and costs no more then $2 at your local electronics surplus store.
WARNING: if you try to solder this fuse understand that it will open at 240 degrees celcius,.. so use cold solder paste or watch your iron temperature (use heat sinks when soldering).
** To test that the thermal fuse is the culprit, just jump/bypass the thermal fuse with a paperclip/wire and hook it up for a few seconds. If you get all of the functions then you know its the thermal fuse!