As long as the barrel's properly stress relieved after it's made, getting hot won't hurt accuracy. And the barrel tenon shoulder has to mate perfect with the receiver's face that's trued square with the chamber axis.
Several folks have shot test groups of 15 to 40 shots with one bullet going down range every 20 to 30 seconds. 600 yard accuracy is in the 2 to 3 inch range. At 1000 yards, accuracy is in the 5 to 6 inch range. Barrels shot this way really heat up.
In one type of highpower competition, teams of 6 people shoot service rifles at 600 yard targets. Using M1 Garands, each one will put 24 rounds down range in 50 seconds. Good rapid fire marksmen will put all of them inside 10 inches. And I as well as others have got burned touching the extremely hot barrel afterwords. These barrels are very accurate; it's the holding area on target that's kinda large.
Don't let a fresh round stay in the barrel more than about 15 seconds else its powder gets warmed up and the bullet will leave faster and strike higher. In shooting 1000 yard matches, I come down 1/4th MOA every 15 seconds after the first 15 to compensate for this. I've waited over two minutes doing this and still shot to call. Once I forgot to come back up to a normal elevation zero and put the next one a bit low!
If the bore's a bit on the rough side, you may need to shoot several shots to fill in those rough areas with bullet jacket material. Those unbalanced bullets won't shoot accurate. After the rough areas are filled, bullets fired afterwords will do just fine.