Provided the rifle, scope & mounts are sound, I have found that the "cold bore shot" is really a "cold shooter shot". I have proved this with/to dozens of long range precision students when I was teaching.
The "clean bore shot" really IS a thing and can usually be brought into the main group by degreasing and drying the bore with 90+% alcohol before shooting. By removing traces of solvent and oil, we can usually get the first bullet to land with the rest of them. That WILL allow your chrome-moly barrel to rust, but doesn't seem to have any effect on a good quality stainless barrel, my own preference for long range rifles.
Regarding the cold shooter shot, most often there is insufficient shoulder pressure due to a loose grip on the rifle. Heavy/fluffy winter clothing exacerbates this issue and must be compressed during the shot.
The shooter fires the first shot and notices the rifle jumps a little more than expected, and oddly enough, that first bullet is out of the group. They tighten up a little for following shots and their group stabilizes. Everyone wants to blame something else, so of course it's gotta be a "cold bore", LOL.
Numerous times I have had students fire a couple shots with one of my rifles, then immediately move over to their own cold rifle and they do NOT experience the cold "bore" (shooter) shot. Go figure.
Those who refused to acknowledge this continue to be plagued by a lost first shot.
The way I had people who shoot one shot at a time for a living handle this is to exaggerate their shoulder pressure for the first shot, which better normalizes it and keeps it in the main group. What seems exaggerated for the first shot is actually where one ends up after realizing their first shot was a little loose.
I teach shoulder pressure regulation by using the firing hand fingers to pull the stock against the should approximating the pressure sensation of a firm handshake grip. This amount of pressure is easy to quantify since most of us shake hands enough to know what a *firm* handshake is, and it is enough pressure to keep the bullet in the group.