My .223 Axis with sporter barrel starts to string them after ~5 shots in a row...but those first 4-5 are quite accurate. I can't say I wait any certain amount of time until unloading another set, just go shoot another gun for 10 minutes and come back to it. Is your 2nd shot after a true "cold shot" where the barrel is at ambient?

You could even get those barrel temp strips and play around with what temp it needs to reach for the groups to tighten back up.