check to see if it has a superseded fan speed resistor fitted.
old style has approx. 15 fins while the new style has approx. 40
if old style fitted replace fan speed resistor
out of all bmws, e39 (your model) are the easiest
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http://www.bimmerfest.com/forums/showthread.php?t=143393
I followed these instructions and reparied myself. Longest time was waiting for the part as I did not want to pay the dealer 2x markup.