Climate Control Fan Runs With Ignition Off

[1983sc]

I have a 2002 X5 4.4i with automatic climate control. Recently I have discovered that after shutting the car off, sometimes the heater fan begins to cycle on and off on it own. It cycles to a high fan speed, easily heard outside the car. Once it caused a dead battery after 3 hours and the second time I caught it before the battery went dead. If I shut the AC/heater fan and control off (reduce fan speed to lowest level and push the fan contol again until the display shuts off) before I shut the engine off, I don't experience the problem. Has anyone encountered this problem? I would assume the ignition switch cuts power to the AC/heater module and fan, like other accessories - e.g. the radio, instrument cluster and heater control display. But that doesn't seem to be the case with my car. Has anyone else seen this problem? Does anyone know the fix for it? I've not been to the dealer yet for fear they will just throw parts at it and hope for the best.