Re: cold barrel shot vs group
If the first shot from a clean barrel is off, then you just shoot a round then go hunting. If you know where the first shot consistently groups from subsequent shots, then you hold over that amount when you shoot the first shot. Either method will work.
Most people use powder that is temperature sensitive, and at long range the cold weather vs. warm weather difference will swamp out any difference between a first and subsequent shot. IMR 3031, which is a common .30-30 Winchester powder, is extremely sensitive to temperature changes.
You don't hunt at long range with a clean barrel anyway, if you have any sense at all. You foul your bore to a consistent result and then go hunting. People who are successful long range hunters have been doing this for a lot longer than I have been around.