From personal experience, I can tell you that temperature has a strong influence on point of impact, and to some extent, precision. Temperature affects the burning rate of most powders, with a few exceptions, and extreme temperatures even affect the priming. Temperature also affects air density and thus, a bullet's trajectory. This is redundant, but, as a rule, higher temps. = higher point of impact and vice-versa.
As Tirador wrote on another post recently, point of impact varies as the day grows longer. This is due to mainly to temperature's effect on the items described above.
Extreme temperatures also affect precision - that is, the rifle/bullet/shooter's ability to repeatedly place shots in the same point of aim. This is especially true in extreme cold weather with rimfire ammunition, which is why "Biathlon" ammo was developed.
I had the pleasure (?) of competing in a couple of "Frozen Finger" (trust me, there other appendages also frozen :grin: ) smallbore silhouette matches in Wisconsin, in January, over the last 2 years, and noticed that my shots were going all over the place, except where they were supposed to go. Other not-so-savvy non-native shooters had the same experience, while the natives, being longer in the tooth, where using Lapua Biathlon ammo and shot "normal' scores. The temperature was between 0 and 8 degrees F. :cb2: