I've never worried about it but some people do. Some people cut out sections of egg cartons to where you have a pretty minimal frame and put eggs pointy side down in those. You aren't turning but you don't want the carton to block them hatching. Also, the chicks produce a fair amount of heat at that stage, you don't want to trap that heat so they cook themselves. A solid egg carton is not a good idea. But one chopped up appears to work.
Personally I would not put bedding or things like that in there. The chicks need fresh air to breathe. Bedding may block ventilation. It may also interfere with the humidity in there. I don't see where cheesecloth would help that much. You still have to clean and sterilize it before you use it again. Maybe I'm missing something?