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Temperature and humidity do effect ballistic coefficient. BC goes higher as they get higher. Sierra's reloading manual has excellent technical explanations. A good ballistics software program could show the effects on a given cartridge's trajectory both will have when they change.
Shooting cold ammo from a cooler will result in a lower muzzle velocity providing you shoot each round as soon as it's chambered. Leave that cold round in a hot barrel more than 30 seconds and the powder will heat up then produce a higher muzzle velocity to require about a 1/4th MOA elevation change up for each minute it's in the barrel.
Hot ammo or cold, its bullets will still go through the ambient temperature, humidity and atmospheric pressure conditions the round's fired in. To see changes in trajectory for different atmospheres, you just about gotta shoot in them then record your sight settings for each one when that particular load's used.
A good barrel properly fitted won't change point of impact as it heats up and rounds aren't left in the chamber more than 30 seconds before they're fired. I've never seen any accuracy change from 20 to 105 degrees F, 5 to 90 percent humidity and 200 to 8300 feet altitude with the same rifle and ammo so I don't think bedding changes any significant amount. But sight elevation zero settings will change.
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Sorry, I have to throw the flag on this one. The 30 second rule and the 1/4 minute of angle adjustment just are not the same for each barrel, bullet, powder, primer, rifling, stock, bedding scenario. Much too vague and misleading of a statement to be published to novice shooters.
For what it is worth (maybe nothing), I have a private 1000 yard range that I use to play on and to tinker with my rifles and loads. I have found the following to be true in all of my hunting calibers:
I work up loads in peak heat and then monitor the point of impact and grouping ability as the season progresses and the temperature declines. So far, I have not had to make any mid-season corrections to the scope due to temperature changes. I suspect that in hunting situations where a rock solid rest is not always available inserts enough error to cover up any changes in impact points due to temperature. When I was just starting out, I did as most do and worked up loads in the cooler periods. Boy what a surprise when the temperature gets high. In other words, it is much easier (and predictable) to deal with ballistic delimmas dealing with declining temperatures than vice versa. My hunting areas range from right at 100 degrees down to 20 or so degrees. I am sure if I were to re-evaluate the loads at the lower temps, that I could tweek them a little. So far, no need to do so. Oh, I almost forgot, I only evaluate for long range trajectory and grouping size in the early morning hours prior to the mirage effect starting which is usually about 2.5 ours after first available shooting light. I then do my pressure evaluation of loads in the peak heat of the day. finally, never, never, never, never, (did I say never), evaluate/develope trajectory tables after mirage has started as it just inserts another unpredictable variable in to the accuracy equation. Specifically, your zero will be much lower than desired. Just the other day, I was shooting my .338 Lapua with moly coated Nosler Accubonds to zero the rifle at 400 yards. I did not pay attention to the conditions on one of my shots and the shot printed 4.5" higher that the other shots. Upon closer review, mirage was present and I deleted the shot from evaluation. And before anyone starts screaming about moly, it tends to flatten the pressure curves and thus the differences between extreme temperature changes. If you have any questions send me an email.
Chawlston