With any new gun, I just take it easy for the first few hundred rounds. I don't get the barrel hot, and clean after each fifty rounds. Gives it a chance to smooth any small burrs and do a little polishing.
I clean new rimfires when I get them and then just start shooting. With a 617, you can use just about any ammo for break in, but I think a nice subsonic round like CCI or Winchester SSHP or Wolf MT would be fun to start.
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Of all tyrannies, a tyranny sincerely exercised for the good of its victims may be the most oppressive. - C.S. Lewis
I clean my firearms with Eezox before shooting them. With the 22 lr firearms, I don't worry about the break in as much since I'm not dealing with extreme pressures and super high velocities.
I normally like to break in a new revo with a couple of hundred rounds of jacketed stuff to smooth the bore before starting on lead stuff. The closest I can come with a .22 is the copper wash high speed stuff. I think it helps to smooth a new barrel. Then you can use anything. CCI Standard works well for me in most guns.
I wouldn't worry about heat. I sincerely doubt you could over heat a revolver barrel if you tried. As with any firearm clean the barrel prior to shooting for the first time. No brush I just run a dry patch through to remove any obstructions.