As far as I know tefloncoating of SS barrels take place under some temperature (around 2-300 degrees celcius ?)
Is it damaging to the strength and hardness of the steel or is the temperature not high enough to be damaging ( don�t want to "neck anneal" my barrel making it softer...).

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UH

No problems with the temperature needed, I remember about 200 degree C. I did it in my kitchen oven. This technique was introduced 20 years ago by McMillan/Wiseman barrels.

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Consider spray painting the barrel. I had a wildcat made up about 14 years ago and I decided that the SS barrel was too bright for deer hunting so I sprayed it with a can of flat black stove paint. It matched the receiver of the M-70 so well that I was very pleased.

Then as time when by the paint got scratched so I over sprayed it. This is a quick operation and you just hold something over the stock or what ever and give it a squirt. As more time went by there were overruns. So now I wiped it all off in seconds with paint thinner.

Bore cleaner will remove the paint from the muzzle so don't let it run down the barrel.

I would never teflon coat a gun.

Now I think this rifle will be a varmint and range gun so the paint is coming off. Easy come, easy go.