The only observable "cold bore" effect I see is when shooting in extreme cold. And in that case, the cold bore effect I am talking about doesn't occur with your first shot of the day, it occurs after your rifle and ammo get cold soaked beyond the point where they will shoot well. Rimfire is sensitive to temp because of the nature of the lube.
I have found that if you shoot a string fast enough you can get the barrel warm enough to improve the accuracy, but it doesn't take long for the accuracy to drob back off again, and I believe that is because rimfire doesn't generate enough heat to change the overall barrel temp, only the chamber and bore temp.
I have also found that the temp threshold for .22lr, at least with modern match ammo, is at a lot lower temperature than most people think. Convention wisdom says that the temp needs to be above 60f, some say 70f, and I have found that accuracy stays the same until about 30f. Things get funky below that, and it becomes rifle specific, but somewhere around 15f most rifles really start to drop off, and it is almost guaranteed at 5f.
Long winded and a little off topic, but I stopped believing in cold bore when I heard an explanation (I believe it was Jacob Bynum) that had logic that really made sense to me: if the temperature of the rifle cause a shift, that caused the second round to be off in relation to the first, then why wouldn't the third round be different that the second and the fourth round different than the third, and so on, because each round heats the barrel up a little more? When I stopped believing in it, I stopped seeing a cold bore deviation.
