My friend did something simliar and the dog locked her out of the car. Is your dog crated or seatbelted in, so that it can change the gears?
I have remote start and the car will run for 15 min, with the air on and locked. I use that feature a lot for when I'm traveling to and from long distance dog shows and need to stop at a restroom. My dogs are crated with fans on the crates.
If this is something you do, it may be worth looking into installing a remote start. BTW, I love the feature, not just because of the dogs, but because I can start the car and heat it up in the middle of the winter, I get into a nice warm car :)