Does having an AC or heater on as soon as you start the car damaging?
Not really. When I was a kid it did because the cars were really basic and didn't have safety features. But today, all modern cars have relays for all this stuff. There is a heater relay and there is an air conditioning relay. So the heater relay prevents any damage from happening when you start the car and will prevent any extra voltage from going to the system and wrecking the heating system or the AC system. That said, it is usually better idea to have everything turned off when you start the car anyways. Because then, all the electrodes in your car are used to start the car and will generally help it start up smoother. But if you forget to turn the air conditioning off, it isn't very damaging.
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