A small cottage cheese or cream cheese or similar plastic container will work as well as a deli cup. Or any small Tupperware type container, too. Just put a few small air holes in it.
Coolers come in all sizes, including some that are just small, cheap, styro containers just big enough for a 6 pack of beer or soda. Or you can make your own by using a cardboard or plastic box and lining it with styro, bubble wrap, or even a blanket or towel. Any of those materials will provide insulation, and keep the inside of the box from changing temps as quickly as the car does when opening and closing doors or windows. Of course, the milder the temps outside, the less you have to worry about that.
If you are depending on your body heat to keep a snake warm, it is important to put it under your jacket or other outer clothes, with insulating clothes on top of it, rather than just sitting on your lap.
I have seen some people carrying reptiles in cold weather with a blanket or jacket, thinking that will keep them warm as it does with humans. Of course a blanket will delay chilling, but since herps don't provide their own body heat, the blanket can only hold in the heat from the house or wherever it was before being taken into the cold. I am sure you know this already, but sometimes we are so used to thinking in human terms that we forget how different herp pets are from ourselves and cats and dogs, etc.