Many off the shelf rifles, have some upward pressure applied at a pad on the for end.
Unless a rifle, is glass bedded, this is a good way to go, to keep groups consistent.
As mentioned previously, each rifle is a beast unto itself. I have a few that will shoot tight groups when it's +45C in the shade and at -40C in the winter. The only difference between the groups will be elevation.
I have a lovely old world Mauser that changes with the weather. The only way I could get that rifle to settle down, was to put it into a laminated stock and glass bed it. I refuse to do that to the original stock.
Try a bit of upward pressure on the barrel, about 4cm from the fore end tip. Not on the sling swivel.
The best way to do this is to hang a weight of about 5lbs from the tip of the barrel and slide in a shim that is just snug. Make sure the action screws are torqued properly before doing this.
This brings up another subject. Torquing the action screws. It used to be pretty common to use a torque wrench to set the action screws. With the advent of synthetic and aluminum bedding, it really isn't needed. Even some of the laminated stocks, especially when they're bedded, don't seem to require it.
The list goes on and on.
I have a Ruger No1, in 338-06, that shoots the first shot 1in low at 100yds and everything else groups tightly 1in above it.
I've done everything imaginable to that rifle, other than taking off the barrel and setting it back one thread and rechambering it, then screwing it back on with more torque.
I've heard this works. I don't know, it's another project waiting patiently in the wings for its turn.