I do shoot water-cooled at the range! I have a wet towel I drape over the barrel in between groups. So...there's that.
(I dont know if what you have described is what I would call "walking". To my mind "walking" would be if the POI changes as the barrel heats.)
I did have a Sako L461 in .222 that shot the same size group no matter how hot it got. But I am not a good witness for this type of thing, my .222's and .223's have all been big game rifles and I dont shoot ten rounds strings.
My thinnest barrel is on my Remington 700 Mountain rifle, which is in 7x57. Its the thinnest barrel and the most accurate larger bore rifle I have, an honest half inch shooter with 139 grain Hornadys. But I dont know how it would perform with a ten round group; I always shoot 3 or 4 shot groups and let it cool down.
I suppose none of this is very helpful.
Why are you shooting ten shot strings? Is this for a "varminting" or a hare rifle? Or in the interest of ballistic science?
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