We have a cooler that we bought at the hardware store but the brand name escapes me. It plugs into to the cigarette holder of your car and it also has a different plug that allows you to plug it into a regular electrical outlet. Last weekend my husband had a 6 hour car trip and he took with him some frozen foods including bread. It was still frozen when he got to his destination. Also, if you plug it in the other way, it will (supposedly) keep food hot/warm although we have never used it for this purpose. We keep this cooler in the car so when we visit various markets we can keep our purchases cool. Something like that would probably do the trick. Oh - my husband just said the make is Koolatron.
My experience with the "plug-in" coolers is that they keep the interior of the cooler about 40 degrees colder that the ambient temperature. If your driving and have the air conditioner running then the internal temp of the cooler is just fine. But if the vehicle is parked mid-day and the interior of the car gets up to, say, 130 degreees, then the internal temperature of the cooler is now 90 degrees.
Several years ago a friend of mine brought one along on a trip to the desert to keep the beer cold. It wasn't even cool. It was lukewarm.
Personally, for something that will probably be in a car for the day, I would go with a regular Coleman/Igloo/Rubbermaid et al cooler and use dry ice.