I wouldn't leave him in the car alone. Then no one would be there to see if the temperature is okay for him.

My advice is: Eat in the car (go through a drive through) or go to a place that has outside tables. Your entire family doesn't need to be shopping at once, do they?

To keep him cool, leave the air conditioner on, and leave some ice packs in his kennel. Also make sure he has plenty of fresh water and put some ice cubes in it.