Re: im moving.
Being a recent college graduate, my hedge was subject to many different moves to and from home and campus. My advice for the actual move is to make sure you know the temperature. Even in the summer I would still have mitten warmers available in case the temp dropped. Also, what temperature is comfortable for you to drive in, might not be good for him. I know that I personally had to fight the urge to crank the AC on full blast. In the summer you do need to worry about heat stroke. The hedge should never be left in the car alone because the temperature can rise rapidly. If possible keep out of direct sunlight. I usually wrapped the cage in a blanket to help protect against wind chill, sun, etc.
As for the actual new home. I would try to keep the cage as similar as possible to the way that it was. This is not the time to rearrange the cage or try a new shelter or food. I usually let my hedge be for the first 24 hours in the new environment so that he can get use to everything. (smells, etc.)
From my experience though, moving is not too stressful on my guy.
Good luck with your move!