We frequently travel with several shih tzu, and they are fine in the trailer (and motorhome before our new trailer). Be careful with your windows. They can destroy blinds if they can get to them to see out. And last summer, one of ours jumped through the screen of an open window when a ATV drove through our dispersed camping location. He was fine when we returned, but could have run off looking for us, or if we'd been in a crowded area something else might have happened.
If it's very hot and not shaded, I will run the A/C. The white noise seems to keep dogs less on edge about when their parents will return.