What your seeing is fairly normal, and nothing out of the ordinary. The browning A-Bolt small barrel really had an effect on temp and shots fired. I know my A-bolt in 308 shoots the first cold bore shot 1" high and 1.5" to the right. After I let it cool, dead center and subMOA for 2 shots. If I throw a 3rd shot, it usually opens my groups to 1.5" group.

Now, I could tear out the original bedding and rebed and monkey around for more consistency, but I know the gun and how it reacts pretty well, and its a hunting rifle, so I leave it alone.