This is very common. And no, it is not the temperature of the car. He is not cold. Preventing him from seeing out will also help because of the lack of visual stimulus to set off his nervousness. It goes away sometimes after many exposures to the car.
Some dogs never get over it.
If it's excitement, there's not much you can or need to do about it. Many working Border Collies will do this before being allowed onto the field for work. We have a couple that will just sit at the gate, shaking like a leaf, in anticipation. I just saw one of the best working dogs in the world not too long ago and before she was let out to work the little thing was so visibly shaking I thought she was going to knock herself over. It's a good thing, not necessarily a bad.