Definitely not a bad idea. I was considering getting a 12v heater from harbor freight if I couldn't get this one sorted out soon.
12V Auto Heater / Defroster with Light
My recommendation to improve your idea is make sure the heater has analog controls and get a Belkin Wemo switch on your outlet. That way you can plug the car in the night before and turn it on without even leaving the house. If low temperature interferes with the switch you can always cover it with one of those insulated hose bibbs/spigot covers.
