Put the cooler with the camera and the film in the trunk not the front. The trunk doesn't heat up very much compared to the front of the car. You can minimize that heating by opening the windows in the front some to let heat out. If you want to use a cooling pack in the cooler, you can keep it from chilling as much by putting a layer of towels over the cool packs below the camera gear. There will still be a cooling effect. Play around with it. I've gone on many vacations with the camera and film in the trunk. No problems.
The camera isn't as available this way as if you have it up front with you while driving, but it'll be ready to go and nobody knows it's there.