Fluting will help with cooling and a heavier barrel will take longer to heat up but it also will hold heat longer. To me, I do 3 shot strings and let it completely cool between. Now on a target rifle that isn't always possible and my 1000 yard rifle is also a RUM and I do not expect it to last anywhere near as long as a hunting barrel. I've always heard when it's hot to the touch you have gone too far. I'd go as far as to say warm to the touch and it should cool down.
My STW will heat up even quicker than the RUM so each barrel depends on contour, bullet and powder going down it, fluted or not, ....
I will say though, 400 rounds through a barrel, is just like aalf said, a result of fast and hard. Not typical of normal hunting barrel shooting but a lot more typical of match type shooting depending on the match.
