I think the cooler would be more dangerous because of the possibility of moisture/condensation getting into the camera.

Cars do get up past 120 degrees esp if the windows are not tinted, I have measured that being in the desert, I suggest you bring your own thermometer and take readings yourself.

The grease and what not will separate esp in shutters, long term effects will be hot/cold where there is condensation, it helps to get large packs of silica gel to minimize water forming in the electronics.

If it isn't a hot day and you park in shade then there is certainly is nothing wrong with leaving a camera in the thrunk of your car. By the way, leaving a camera anywhere else in a car is an invitation for some lowlife to do a smash and grab.

I have for years carried cameras and kept them in my car during summer. I always have my cameras with me, even at the burn. I've never had any issues, even on-playa. The heat and dust haven't yet had an impact on the performance of either of my two cameras. I think that after long periods of time that heat might be an issue, but for most cameras I think that occasional exposure to heat shouldn't be much of an issue. Throw a white towel over your case. This both conceals the nature of your case, as well as reflecting the bright sunlight off darker surfaces.