Airguns don’t really get hot, so I use the term “cold bore” to refer to the first shot. Like the first shot of the day at a target, for score, with no sighter shots. Though it could also mean shooting at a new target distance with no sighters.
At the recent EBR Bigbore match, it had been four days since I last shot the rifle. I unloaded it from the van, purged the reg, and proceeded to shoot the match. Every shot I took that day counted for score. That would be considered “cold bore”.
Once I sight in my rifle, preferably it stays that way for the long term. I sight in my airguns at the trajectory apex. That happens to be 37 yards for my 7mm. I use that because it’s constant even with different atmospheric conditions (barometric pressure). My range is near sea level, but most of the competitions that I attend are at 2000ft +. A 100yd sight in is about as far as I’d feel comfortable with (as long as conditions were calm). Much farther than that and you need to redo your sight in when barometric pressure changes significantly.