It depends how far. If it's a short drive, just a box with a towel would be fine. If it's a longer drive (more than, say, 30 min?), you might want to wrap a hot water bottle in a towel and put it underneath your dragon to keep him/her warmer.
Typically an enclosed box (shoebox, critter keeper, something along those lines) with paper towel and/or shredded paper works well. As previously suggested, for longer trips in cooler weather (below 75), adding a hot water bottle to the container or resting against it can help keep your baby warm. You can also get 40 hour heat packs, or hand warmers, and put one of those in a paper bag and add them to the container as well.