I take the batt. out and put my bird in a bag and highly recommend it to anyone who is storing their car in unheated storage. I also recommend having 2 people to put car in as plastic bag is thick and easier to maneuver for 2 rather than 1.
Your car will be as clean when it comes out as when it went in plus, bag keeps rodents out and moisture out. Oh I'm sure rodents could chew threw it but for some reason they don't or haven't yet .