I first enquired about this last November, and had helpful responses
explaining that there were two major causes of problems with the
heater control unit:
#1 A capacitor in the unit itself
#2 A 'final stage resistor'.

I'm embarrassed to say that I've only now got my act together on this.
Back in winter I did remove the unit and obtained a replacement
capacitor with the intention of fixing it myself - but chickened out,
nervous not about the dismantling and re-assembly!

I've been living with it ever since. Up until a few weeks ago it was
bearable, but it got so bad recently that yesterday I sent it away for
repair of fault #1 (£45). Now await its return.

But it seems I *also* have fault #2. The fan is erratic, and has been
so for some time. For instance, directly after the unit was removed,
on switching on the ignition the fan was blowing (quite strongly),
which is the correct default. This morning, nothing. (That squares
with what I was getting in recent weeks, except of course that in that
case the scenario was complicated by the erratic behavior of the
heater control unit too.)

Last time, Jeremy said:
"On the E39 similar symptoms may be experienced if the "final stage
resistor" (aka hedgehog) fails - part for the E39 is circa £50 IIRC
and quite DIY-able (although fiddly)."

And JB said:
"I've come across this same problem [#1] and also one with the sensing
thermistor several times."

Are these two, "final stage resistor" and "thermistor" one and the
same thing? I suspect so, as a thermistor is essentially a resistor
which changes its resistance with temperature. Or is it in fact a
*diode*, which I've also seen mentioned? (The voltage drop across a
varies with temperature, and is often therefore used as a temperature
sensor.)

In either case, can anyone give me full details please? In particular,
is the component accessible? And can I get a suitable thermistor (or
diode) myself, rather than pay no doubt exorbitant BMW prices?

Any practical help would be appreciated please.