this topic is as controversial as "how much can i tow with a half ton?!?!"
Have some respect for your campground neighbors and communicate with them. if you find yourself needing to leave your pets in the camper for a part of the day try to be aware of whats going on. try to book sites in shade under trees to help control the heat. if your trip keeps you away from your camper most of the time leave the dog with a family member for that trip.
If you need to run to walmart turn on the radio and A/C. Your dog will be just fine.