While I can't speak to any phenomena involved when it comes to comparing a cold and warm barrel ...
I can offer an observation based upon my experience on the firing line.
What you describe isn't an uncommon sight to witness when watching many LE & CCW folks fire their first few rounds during a course of fire.
Then the shooters seem to 'warm up', settle down to business and demonstrate better accuracy.
I remember reaching the point in my training when my first 1-2 shots were finally consistently accurate (fired 'cold', first thing during a range session or qualification course of fire). Turning point. Confidence booster, too.
Reminded me in a way of when I was a young martial artist and my first punch or kick might be a bit wild and less controlled than I would desire. Further training and skills development eventually corrected that problem, too.
Working to overcome the 'startle reflex' (anticipating the felt recoil and 'fighting it' before it's occurred, for example) and settling down to demonstrate a good, consistent initial grip and trigger control seem to be common issues for many folks who either don't get in much consistent training/practice, or don't have the opportunity to receive the assistance of an instructor to resolve some bad habits (or simply improve their skills).
Shooting is a perishable skill.