If barrel heating is the sole cause of the group dispersion, the dispersion should be vertical. If it is other than vertical, keep looking. We assume at this point that all stock and scope screws are tight, that the scope is not defective, the barrel channel is free floating, and quality ammunition is grouping 5" at 100 yards using good shooting procedures in calm conditions.
Examine your targets and see if the holes are round or elliptical. Is closing the bolt on factory rounds difficult? Examine your fired brass to determine if there is evidence of chamber irregularities. Determine the amount of bullet jump.* Do any of the fired rounds show signs of high pressure, such as extractor marks on the case head or do you recall any round that resulted in a difficult bolt lift? Check the muzzle for damage or irregularities at the crown. See if you can detect movement of the action in the stock. Clean the barrel down to bare metal with a good copper removing solvent like Sweets, then start again with an absolutely clean, lightly oiled bore patched dry.
Fire a shot at the target, wait until the barrel is back to the ambient temperature, then repeat for 5 rounds. Is the group size reasonable? Now repeat rapid fire shooting as well as you can, but allowing the barrel to heat up. There are a few things you need to do at the same time here. First, determine which shot goes where on the target. Second, as the barrel heats up, does it remain free floating? If not mark on the forearm where it gets tight. Finally, record what the group size was and how it compared to the slow fire group. Are there any rounds that did not print on the target?
* Check the bullet jump . . .
Pull a bullet part way out of the case. Push the nose of the bullet into the muzzle of the rifle and turn the cartridge to scribe a line on the bullet, this line shows you the ogive of the bullet, and you are concerned with the distance from this line to the rifling. Color the bullet with a magic marker. Chamber the round (the bolt may close with difficulty) then eject the round. Repeat with another round but without pulling the bullet. The long round should show rifling marks on the ogive of the bullet, and the factory round may not show any, and if it does it might indicate a throat that was not cut to proper length. The difference between the mark on the long round and the ogive of the factory round indicates the amount of bullet jump. If the barrel is chambered within normal tolerances, the jump will have a minimal impact on accuracy, but checking it will be useful to ensure that dimension the chamber is within spec.