Put a sturdy stick in a box and secure it so it can’t roll around. The box should block out all outside light, if it does he’ll sleep the whole way. If you can’t swing that just do your best to eliminate as much visual input as you can. All the fast unfamiliar objects jetting past is what stresses them...
Think about the way chameleons are shipped by breeders to customers. They spend up to 24 hours in a small box being tossed around by the freight company. Three hours in a box in a car will be just fine. Don't worry.