The fan should only be 'on' when car is running, and not turn on after you removed the key.
-If for any reason the thermostat is not working correct, you can risk that the fan will just continue to run, until no more volts on battery.
-When any car stops, the heat will always rise.. -since there is no waterflow anyway, it does not help that fan turns on (well the air is cooler, but not the engine)
