Barrel heating
If you have a thin barrel, it might get warm, but with 22 LRs they really don't get hot, at least I haven't noticed that on my two thin barrelled rifles. 0.920 inch bull barrels you can shoot all day and they seem to only get slightly warm.
If the barrel isn't too hot to touch, you probably aren't going to see any deflection or harmonic variations with a 22LR even with a thin barrel.
Now with my .270 Winchester, the barrel gets really hot - so hot you can't touch it. You can see the effect on its thin barrel on the 4th shot. After 3, the 4th and 5th shots move out further and further to the right at 2 o'clock. That turns tight groups into "good but not great groups".
But with a hunting rifle, you're not supposed to be firing more than one anyway. The first two or three are well under 1 MOA with ammo the rifle likes.