Passenger compartment temp is maintained by blending cold air from the
outside with warm air that has passed by the heater core. How much air is
blended is determined by a thermostat. Kind of like the thermostat in your
house. You turn the heater on (in your house) and the heater blows how until
the thermostat is happy, at which time the heater turns off until the
thermostat decides it is cold again. In your car, the action is a bit
diffferent, blending baffles open to a specific location to allow the proper
blending of air to achieve the desired result. The air that enters the cabin
is a constant, unlike the air entering your house due to the activity of the
furnace. The car's heat source does not turn on and off, as happens in your
house so the thermostat (cabin) changes the baffle position to alter the
amount of cold air that is blended with hot air to give you warmth at a
desired level. To complicate matters a bit, (my car, and I assume yours too)
there is a temp control for both left and right sides of the car. By your
description, I assume you are complaining that both the driver side and
passenger side are cold. This points me toward the heater core itself, or
its associated plumbing, as being clogged. On my car, I can set my side to
70 and my wife's side to 80. As a general rule, the entire car gets hot
eventually, but her side gets more hot sooner. This would happen if there
was a thermostat, or more than one, in the cabin that operated baffles.

If the thermostat governing your comfort stops working, the result could be
improper mixing of the air sources, and you get a cold cabin as a result.

The life support system basically lives behind the center of the dashboard,
straddling the transmission hump. I've only seen one, and it was very large.
It comes out as an assembly, then the component parts are removed as needed.
I don't know how much of it can be serviced with complete removal of the
system.

I once had a car ('65 Ford Mustang) that had rusty water in it. The heater
blew cold even though the fan whirled around furiously trying to do its job.

I got tired of being cold, and connected my garden hose to the outflow
hose -- the hose the sends water back to the engine after it had gone
through the heater -- and lots of rust and gunk came out. I connected to the
outflow hose because I didn't want to push any blockage further into the
core, making the blockage even worse. Today, I would be branded a polluter
on the scale of the Exxon Valdez for pumping rusty water onto the street,
but it cured my problem of poor output from my heater.

My suggestion is to flush your cooling system and see if you can get your
heater to come back. My old Ford is completely different than your modern
BMW, but I hope my experience helps guide you to the least costly service
activity. I like to do the cheap & easy stuff first, and save difficult &
costly for later.