If it doesn't blow high speed right away, that can be normal. Unless the system has cold (or hot, as the case may be) available, you won't get full fan speed.

Apart from that, incorrect fan speed is most likely caused by the FSR. It usually fails in a mode that leaves the fan on. It is a solid state component (not just a resistor) and as noted above, is easy to replace.

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2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue