Well all I can say is that I have been shooting pictures (all formats) for over 40 years, and professionally for over 32 years, and I have never felt the need to take special measures to keep my film cool when traveling. Yes, a closed, parked automobile in the summer can get quite hot in the passenger compartment due to the heat gain thru the windows. Hint: Leave a window down a tiny crack helps prevent excessive heat build up. The trunk (boot..in UK) is a better place for surplus film. You do what you like, but carrying a dozen or 2 rolls of color and b/w film around should not be a problem for anyone. Like I said, film is comfortable for reasonable lengths of time (weeks) at any temperature you can tolerate. Long term storage is another matter.
What you say really does make sense. Maybe I'm worrying for nothing. I have no trunk (I drive a truck) but I always, always leave my windows cracked so that I'm not gasping for air when I get back in the car. I may just keep the film in my lunch pail with one ice pack which will maybe take the temperature down from 120 to 80 degrees. Either way I think it will probably be OK because, as you say, it's not long term storage.
Now if I could just get a hold of a pair of testicle refrigerators...
They give us those nice bright colors
They give us the greens of summers
Makes you think all the world's a sunny day, oh yeah.