Years ago when M&N lubricant was made, this lubricant required at least three shots fired on each string before it would start to group:
- In a group match, I'd fire three or four into the sighter to judge wind and then go to the record target.
- In a score match, again I'd fire three or four into the sighter for wind and then go to the record target.
I've seen the results of testing where thermocouples were attached to a Savage 12 BVSS .308 above the chamber and both long and short strings shot. The rifle grouped best when the barrel temperature was between 122 and 125 degrees. This suggests barrel temperature affect lubricant qualities.
In colder temperatures, the barrel will take longer to heat up and may not get to the internal temperature affecting the lubricant in a match's time limits that it needs to shoot well.
As Ric suggests, NRA Alox/Beeswax would be a good starting point. You could test to see it the rifle comes back to grouping after a series of twenty or even thirty shots when the barrel is warm.
I'm using Javelina Schuetzen Lubricant which is very soft to start with. I may be avoiding this phenomenon by chance. I have testing to do these coming months when the temperatures will be in the forties and fifties, I'll see what I can observe.
I'd like to give a better answer, this is all empirical evidence.
Farm boy from Illinois, living in the magical Pacific Northwest