I had to take my cham with me last weekend for a several hour drive. On the way up I left her in her cage and covered the whole thing with a towel, but that definitley did not work. She was scratching at the cage the whole time..she was very upset. That weekend I heard of the paper bag method, and used that for the ride home. it worked much better. I sealed the top of the bag so it was dark, and she slept the whole way. Even when I got home and went to put her back in her cage she didnt wake up till i touched her. She seems much less stressed with the paper bag.
How big is your cham though? Mine is just a baby so she fit in a paper bag just fine. But if they are big im not sure how well that will work.