Just recently had this issue but on my 2003 E39 M5, usual culprit is the FSU (Final Stage Unit). Fairly cheap part to replace but tough to remove and re-install if you have big hands...

Usual symptom is sudden increase/decrease of fan speed on the AC/Heater blower...

Search for FSU here and I'm sure you'll find some threads talking about the same issue on the E53 X5.

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TQ2K


'04 N62 - Alpine White/Truffle
'03 S62 - Petrol Mica/Champagne
'97 S52/4/5 - Alpine White/Dove
'91 M42/4/5 - Brilliantrot/Tan