I've always done the shoot and clean for 20-25 rds and then go to 3 shot groups and clean for 20-25 rds. This has been for factory barrels and has worked fairly well over the years. I do this even with used rifles that I wasn't sure of the round count and/or abuse. Did it help? Not sure as I've never done a "scientific as found, as left" scenario. After this "break-in" period I just go straight in to serious load development.
The best or easiest barrel was a Savage 112, 6.5-284 Norma. The very first 3 shots (and 3 shot group) was a .3" group. It just got better with more shooting and more cleaning.
The worst or hardest barrel was a Remington Sendero, .300WinMag. It hovered between 1.0-2.0" for 100-150 shots. I was thinking I had a lemon but once it started it ran .5" MOA with everything, until I traded it off.
For the custom barrels, I follow the mfg's directions. Shilen, Pac-Nor and Lilja all have their respective directions. Lothar Walther said no break in is necessary as their barrels are hand lapped before leaving.
For cooling barrels; I have used wet/damp rags, from ambient temp. bottled water. A couple years ago I put a 12v mattress pump together with various hoses from a local hardware. Total cost, IIRC, was less than $40.
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I attach the respective Hornady modified cases in the hoses for the particular rifle(s) I'm shooting that day. With this setup I can cool two barrels while I'm in the bed of the truck shooting another one, or two. If I only have one barrel to cool, I just stick a fired case in one of the tubes.
