FSR(also known as hedgehog for its appearance) is your final stage resistor and is located behind the fan you are hearing.Its a known culprit for discharging your battery.It overheats and stays on ,even wheh the car has gone in sleep mode.Your car being a 2002 ,you will have the old design FSR with few thick spikes and Bmw has subsequently replaced with another part ,with more thin spikes,which is more efficient in dispersing heat.
There are various threads on this subject,,this is one http://www.xoutpost.com/bmw-sav-foru...r-fix-diy.html