Bart B, that assumes that the tension on the string remains constant, a combined function of both the key, and the temperature - temperature will affect both the length of the string, and the shape of the neck.
Which actually is a good parallel for the rifle.
603Country, sometimes a discussion of theory helps people understand why the different, practical methods work, or which of the practical methods is more likely to apply.
Whether the OP needs to do anything is another matter. He has a hunting gun, not a target gun, and apparently his groups are fine until he has fired several magnum rounds. He just needs to allow cooling off time between his groups, when sighting in the rifle, and may not need the expense or effort required to free float it or fully bed it.
If he were planning on being able to use it for extended shooting scenarios, that would be different.