These types of faults can be very hard to fine.
The fact that the fan stays on suugests that something is not shutting down correctly. The draw from a fan motor wil flatten a battery very quickly.
A first thing to try may be to disconnect the battery for half an hour or so - this will at least shut all the electrical systems down. The electrical sometimes get upset when the battery goes flat.
Charge the battery and reconnect it and see if it happens again.

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'02 X5 3.0d, Auto, Topaz Blue