Are you saying that by shot #3 it starts to group tighter?
As you are doing 2 shot cold bore testing-- I was assuming that by the 3rd shot it grouped better.... but maybe I'm reading into it.
I wouldn't say that 2 shots of 308 has totally warmed up a barrel enough to start any significant thermal expansion--- it takes 3-5 shots of my 308 to really start feeling significant heat in the barrel.
Have you done this "2 shot cold bore testing" with other firearms to make sure your not "warming up" the shooter? It odyen takes a few shots to het me warmed up, especially if I change firearms-- I need to get used to the trigger, stock fit, recoil, and weather conditions of each particular rifle session before I really start to shoot well. --- just a thought