Actually, when you think about it, your cooler could become an oven!
If the interior temperature of the cooler finally reaches the ambient exterior daytime temperature on a hot day the insulating capabilities will work in reverse!
The heat will now remain trapped in the "cooler" overnight even as the ambient external air temperature cools down. Thus keeping the film and gear exposed to higher temperatures than if they were not "protected" in the "cooler".
Futhermore, the next day, the "cooler", now already at an internal temperature greater than the exterior, will at best reach equilabrium with the ambient external heat when the latter rises. It will then further heat up as the day goes on.
And, if you are travelling during a period of ever-rising temperatures - such as from early to mid-summer or from more northerly latitudes to southern ones - the "cooler" will eventually have lost all efficacy. And even this brief exposition fails to take into account the, as yet unmeasured, but ever-increasing deleterious effect on film efficacy due to global warming.
In addition, as you open and close the "cooler" you may well introduce unwanted moisture in the form of humidity. This would be espescially a problem if travelling from drier areas to more humid ones. Once introduced to micro-environment of the "cooler" this humidity will become "trapped" and may result in a percipitate. Not being a chemist, I cannot but naively speculate of whether such percipitate might begin to "interact" with the polymers of the styrofoam "cooler" - perhaps as a result of the outgassing of various compounds from the now "doomed" photographic film?
Equally worrisome is that attemps at mitigating the "oven-temperature" issue by migrating the so-called "cooler" from your vehicle to your (presumably air conditioned) hostelry room could cause condensation and introduce a micro-environment conducive to the growth of fungus and mold.
As a photographer, I am certain you are well aware of the problems fungus and mold can have to lenses and other camera gear.
All in all, if I were you, I would indeed be extremely cautious in considering your Summertime photographic excursions!
[NOTE: The above is intended to be read with one's tongue entirely in cheek!

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