Reptile Basics sells reptile heat packs that only go to 100F for like $1.10 each. I ordered a few to keep for just this sort of occasion! I would be afraid the regular hand warmers will get too hot, they get pretty darn warm.
Edit: Yep, look on the CVS website's warning page: "Heat pack can reach up to 129 degrees F". You may be able to make it work fine by just taping it to the outside of the box, but be careful! It would be better to get one of the reptile packs.
If I were you guys and didn't have a heat back, I would just bring my thermometer with me and set the car heat so that it's in a safe range --- 85 or so. And definitely don't put it in the floor, that's where all the vibrations and noises will be.
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