That's tougher with a baby. They need a lot of attention and feeding. Generally they can handle car rides pretty well but that's much easier when they're older. If you can leave him in his familiar environment with someone who can check on him regularly and give him bug feedings every day it will probably be best for him, especially if it's only for 10 days.
If you do decide to bring him with you, I would get a pet carrier that you can strap into a seatbelt. These offer soft bottoms and plenty of ventilation. They do fine at normal car temperatures but you may want to have a hand warmer or two so you can put it under a towel or blanket to keep him warm if you stop for meals. Keeping a tub of black soldier fly larvae is the easiest for travel since they just do their thing in an easy to carry container. I would bring an adjustable lamp stand with a dome fixture and a good mercury vapor bulb (PowerSun 100w, MegaRay 100w) that will provide a good basking site for him while you are at your destination. A large clear plastic bin should do for temporary housing. You could use a foldable child's playpen too but I'd use one that has solid sides at least near the bottom because they are pretty good at climbing up the mesh.