Completely deflated, you're going to want to strap the tubes in somehow. Otherwise, they'll flap around and possibly damage themselves (or other stuff, not excluding your sanity.)
My longer trips usually involve pretty wide temp swings, (though not going through the altitude changes you did); I leave the tubes a bit soft at home, which allows for some expansion as the temps warm. When I get out of the inland valleys, the tubes go really soft (to the point of nearly flapping), but it's generally a short distance to my destination so I don't worry about it.
Note that you get a substantial amount of cooling from the air movement while driving; on a warm sunny day you'll feel the tubes firm up as they heat when you stop. Gotta watch that, too.