Just a few of observations.
Air density effects more than just patterns. It also adversely effects penetration by putting more drag on the pellets.
Temperature effects the velocity of the shot not only because of the fact that the air has more density but powder burn can be adversely effected.
Drag, as has been noted, is also caused by "gunk" in the barrel. Any drag can effect performance. Clean barrels, by and large, shoot with more velocity.
Velocity and penetration are not always the "friend" of good patterns. Slower shot, coming from a clean barrel may pattern better than faster shot coming from that same clean barrel.
Observing wads from shells shot can tell you a lot about how they interact with the bore and the choke. The heat generated at setback effects the expansion of the wad more than atmospheric conditions.
Shells that have been held at very cold temperatures, such as those in goose pits and duck blinds or those left outside in hunting coats in cold weather, may lose a lot of energy. Think about that effect when combined with the steel shot used by many hunters for waterfowl. It means less energy at the target.
Big bores like those on the Mossberg overbored guns, the Invector+ barrels and the Pro-Bore from Remington barrels work very well to lessen the drag on wads.
The engineers at Olin/Winchester did work on the effects of atmospheric conditions on shotshells years ago and it remains the definitive study. It's an interesting read.
Thanks,
Clark