At no time should a cue be leaned up against a wall, table or any other object for any length of time. This practice invites warpage and many other problems. A two piece cue should always be broken down and stored in a good case when not in use. Never leave your cue in the trunk of your car, even if stored in a case. Sun rays will heat up the trunk causing the wood to eventually dry out.
Cold weather is equally bad, because moisture can form on the cue.
When exposed to warmer air the moisture ends up being absorbed in the cue. This will cause warpage.