I'll second that - If you really mean it stops blowing completely, look at the fan speed resistor (fsr) or fan/blower itself. The rear has its own blower, BTW.

There are threads here on testing the fan without removing it.replacing it is a big job.
I'd consider the FSR first though. Very common failure and not hard to reach.

__________________
David.X5
2001 X5 4.4i Sport
SOLD! at 160k miles