How sensitive to temperature and barometer changes is the POI?

I would rule out everything involving the gun and the wind first. A crosswind on a moving gyro can make the gyro go up or down (I think). The crosswind can have an up or downdraft bouncing off the house. If shooting a springer, first cold shots will go to different POI, etc.

30 yards seems close for barometric pressure to matter.

Well, changes in barometric pressure do affect pendulum clocks, but those are parts-per-million kind of differences.

Are you shooting that RWS 34 you had? I could see a springer showing more sensitivity to air condition changes, but others will have to chime in with data. I know altitude affects them, but I don't know how much.

Once I tuned my D460 and lubed with ultimox #226 I find very little difference between cold shots and warm shots but my D460 was lubed with all synthetic grease

The quick answer is yes, there can be significant changes due to temperature, barometric pressure, and humidity. Warm air is less dense than cold air, low barometer (higher altitude) is less dense, and humid air is less dense than dry air.

He said both times the rifle was the same temp, ie inside.

I’m going with mostly the wind difference or first cold shot or operator difference. Some combination of those.

I agree in principle with what has been said so far.  However I think the important part is the degree to which one can expect the temperature and barometric pressure to affect things.  A vertical change of 1 to 1.5" at 30 yards is an awful lot for the differences you described.  I don't have nearly as much experience with springers as with PCPs but I suspect there is more at play here than just the temp and BP.  Being dressed differently, for example, will influence the recoil so that may be a contributor.  You sound like you are familar with the factors that influence springer repeatability but whenever I see an otherwise inexplicable vertical shift, I immediately look to where exactly on the forestock it's being rested.  With most springers, I get the best repeatability by resting it right at the rifle's balance point.  If you aren't 100% supremely confident you were resting it exactly where you always do, I suggest you mark the resting point with a piece of painter's tape and do two test groups with it rested an inch fore and aft of that.

I agree in principle with what has been said so far.  However I think the important part is the degree to which one can expect the temperature and barometric pressure to affect things.  A vertical change of 1 to 1.5" at 30 yards is an awful lot for the differences you described.  I don't have nearly as much experience with springers as with PCPs but I suspect there is more at play here than just the temp and BP.  Being dressed differently, for example, will influence the recoil so that may be a contributor.  You sound like you are familar with the factors that influence springer repeatability but whenever I see an otherwise inexplicable vertical shift, I immediately look to where exactly on the forestock it's being rested.  With most springers, I get the best repeatability by resting it right at the rifle's balance point.  If you aren't 100% supremely confident you were resting it exactly where you always do, I suggest you mark the resting point with a piece of painter's tape and do two test groups with it rested an inch fore and aft of that.

Didn't read OP until the end, so, yes those things can affect POI, but no probably not that much.  I agree with the above.

And there is your group shift.

My theory is start with the easiest things I can control first. I won’t notice the 1/16” barometric pressure will have nearly as much as my variables.

And there is your group shift.

Not really. I guess my explanation wasn't very good. I'd already made the rest change on my previous shooting session and everything had stabilized. In the last session that had the group shift, nothing changed from previous except a medium weight sweatshirt (and the weather).

I guess I'll chalk it up to the cranky/fussy disposition of a springer that requires everything to be utterly perfect, including the shooter before it'll produce. Even then it might decide to not co-operate. Some enjoy the frustration and challenge. I don't. But I'll keep messing with it.....for a while anyway.

OK, next shooting session I'll wear a T shirt, leave off the sweatshirt and see what happens. However if springers are that fussy about clothes, it's a wonder any squirrels get shot since that hunting season goes from very warm weather to quite cold.

Speaking of shoulder fired arms, I've never had that problem with powder burners. Or maybe you were referring only to air guns. I've never done 300 - 500 yd PB bench rest shooting so maybe it makes a difference there. But at 100 yds, no problem.

OK, next shooting session I'll wear a T shirt, leave off the sweatshirt and see what happens. However if springers are that fussy about clothes, it's a wonder any squirrels get shot since that hunting season goes from very warm weather to quite cold.

Speaking of shoulder fired arms, I've never had that problem with powder burners. Or maybe you were referring only to air guns. I've never done 300 - 500 yd PB bench rest shooting so maybe it makes a difference there. But at 100 yds, no problem.

To be fair, we're talking 10-meter and other highly competitive target shooting where any deviation from 1 hole @ 10m or the equivalent at longer ranges means losing the match.  Different clothing will inevitably change your hold:  the bulk of it at your shoulder and elbow bend, and so forth and so on.  And that will affect the consistency of your shot, whether shooting a .475 H&H or a 5fpe airgun.  Wouldn't have much effect in benchrest because you aren't holding the rifle, but there are free-position shooting contests that demand close to benchrest accuracy.

With a springer, changes in hold can more drastically affect your shot, but don't kid yourself that clothing makes a difference, however slight, with every long arm you shoot.  A shooting jacket helps support muscles, improve steadiness, and reduce fatigue.  But, along the way, they also provide clothing consistency and target competitors at all levels and all types of rifles use them.