Heating/Blower Fan on 2002 BMW 325i

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The heating and air conditioning in my car works fine; however, when I shut the heat OR the car off, the fan continues to blow until the car battery dies. I would like to confirm that this is actually a heat blower issue since the heat works. Why is this not a relay/resister issue? What is the estimated cost of such a repair and the time involved in dismantling the dashboard for repairs. We turned the unit off to avoid killing the battery; however, it is 23 degreess. I need heat in the car.
(1) Answer
My experience with technicians who know BMWs is that even the AC system is really complex--it has a computer that is relatively robust dedicated to its operation. This means that you'll likely be best off with some professional help. The short answer is that it's not a relay problem because BMWs are so complicated they tend to have dozens of relays.