FWIW, my own sunny summer "instrument in car" experience:
If the instrument is well-wrapped in blankets or other insulation, maybe stuffed under duffel bags, AND away from direct sunlight, it will take an hour or two in a parked car to raise the in-case temperature by a just barely noticeable amount. Note that I do like insulated case covers which, for mandolin, translates to a padded/insulated 3-racket tennis bag. (Some such bags have zippers too short to let a hard mando case in). When available, even partial tree shade does help.
Of course, I've never tried this in, say, Death Valley; probably never would!
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