I was getting out of my car today and my blower wouldn't shut off, even after I shut the car off and ran my battery dead
Blower on 2004 Chevrolet Malibu Maxx
My 2006 Malibu Maxx recently did the same thing. It turns out that it needed the thermostat changed in it. A week later, my transmission went in it.
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It is most likely your heat controle sensor, I have had my replaced. I would turn on the car and the fans would just start going even if cold, my temp reader in the car would not move after driving for 30 minutes. I would get it looked at soon