A cold face washer for bub to suck on.

A spray bottle of water you can spray over the top like a mist can help.

Do you have covers on your windows?
i was going to suggest the same thing. maybe get some shade cloths for the car windows, and then take some water spray bottles that you can spray when he seems to be getting too hot? it's hard when they're like that, DD was like that as a newborn, was just constantly sweating, but was also a baby that needed to be swaddled....Lol.