This car has was diagnosed with a defective heat exchanger, also know as a heater core.
The heater core as used in this BMW’s climate control has hot engine coolant flowing through it during operation. The heater core, which is comprised of a an aluminum core and nylon tank ends had developed at leak at the interface. This area is often sealed with rubber o-ring which fails after long term exposure to heat and coolant.
Once the o-ring seal fails, coolant will begin to seep out of the heater core into the heater box producing a strong burning smell from the dash vents. This can lead to long term problems if the antifreeze gets onto or into control motors, servos or air direction flaps. Like most heater cores this unit is somewhat buried in the dash, necessitating a fair amount of disassembly to remove and replace. Its always a good policy to flush the cooling system at least every two years, or 30,000 miles, and to use a quality antifreeze with corrosion inhibiters.