Sorry but there is no "cold bore". This has been disproven by many shooters, and the cold bore theory doesn't make sense from an engineering standpoint. Go to any top precision rifle training course in the USA and they will tell you that it is a myth. An instructor with C/S 66 has disproven this in front of a class recently as well. Frank Galli has disproven this. Numerous shooters (especially in the US) have disproven this.
None of my rifles have a "cold bore" shift. Sometimes I've yanked one, but there is no correlation between a cold bore in any of my rifles and a shift. Funny enough, none of my close shooting friends experience a cold bore shift either.
Cold bore is actually a cold shooter, or it could be the difference between a fouled and unfouled bore. But it's not from the barrel or chamber being "cold" - that simply doesn't make sense.
I will state that a good quality barrels will obviously be important in consistent and repeatable precision (and just as importantly, a good chamber job). This is why I suggest barrel brands such as Bartlein, Krieger, Benchmark, Brux, Rock Creek. You get what you pay for, and cheaper barrels are cheaper for a reason.