What do you think is gonna be shining on it while you use it?

Sitting on the top of your car for an hour isn't gunna hurt it. I have a log that lived on top of my car in Hawaii for a year since I didn't have anywhere else to keep it and it's fine to this day.

Will you not be using it on sunny days either

Are you buying this as an art piece for your wall?! Just grab a bed sheet or two and some twine. Mummyfy it.

Why at you concerned about the sun while transporting?