I used to fit a 9.5' surfboard, a carbon fiber road bike, business clothes and casual clothes inside my Prius for an annual business conference in San Diego. Temps outside here were in the 100s and in the mid 80s in San Diego. For sunshine, I just put a dark towel or blanket over the top where it was exposed and I always leave the windows slightly cracked when parked in the summer. Never had a problem.
Bows are far simpler (especially take-down bows). If it's warm, wrap it in an old comforter and keep it out of the sun, preferably down low on the floorboard.
Of course, I was raised to not worry about nicks and dings on gear. Like with pickups, they're marks of character and use, not flaws to be avoided. So if you're the type who babies his gear or worries about a scratch on your car's paint job, don't ever listen to my advice on this kind of thing. If you spent $1500 on a bow, then make sure you spend a little more on a good, well-insulated case for it.