If you use a pillow case, make sure you turn it inside out and inspect all of the seams for any loose threads or small holes. Snakes are good at finding those and exploiting them.
I usually don't put my snakes on the car floor, mainly because of the vibration's. I normally keep mine on the front or back seat. If you do have to put your snake on the floor, fold up a blanket for the tub to sit on.
If the heater in your car works, just keep a thermometer with you and keep the temp in the car around 75-80ish.
If you want something for emergency heat in case any problems come up, I suggest getting a few of those hand warming heat packs from Wal-Mart, in the outdoors/sporting goods section.