It's really not a good idea to leave your car running with the a/c on either. I can't recall the details of where this happened, but a few years ago a Police officer left his K9 in his patrol car with the A/C on while he went for lunch. Department policy. While he was in eating, the engine on the car died, and so did the dog.
Wide open windows sadly will mean a stolen dog.
Best to leave the dogs at home. That said, I always had to take my older girl with us, and we only shopped in placed with underground parking in the summer, or one of us stayed in the car with her.