Keep it away from liquid or dirt. Your car trunk may be convenient, but an exceptionally bad area to keep your parachute. Not only can it be very hot but batteries or jumper cables with battery acid residue may have been or still are kept there. Battery acid can mean instant death to your parachute. I would look for a different location.
Mice like to chew up the parachute for nesting material and can do severe damage in minutes.
Put everything in the carrying bag or other suitable container to protect it, such as a heavy duty plastic bag. If you have any doubts about the condition of your parachute contact your rigger or the manufacturer. Most manufacturers' manuals for parachutes in use today discuss how to perform a preflight inspection and I urge you to become familiar with them. If you do not have a manual, get one from the manufacturer or copy a friend's, if they have the same type and model of parachute. This could be an indication of damage to your parachute inside.