A top quality barrel will not shift POI as it heats.
The Stevens is about the cheapest centerfire bolt action rifle on the market. The fact that they tend to shoot as well as rifles costing 4 - 5 times as much tells you that money spent on a factory rifle is not proportional to accuracy.
It is a sporting/hunting rifle. It is not intended to resist the heat of firing 20 shot strings, it is not designed to render benchrest accuracy, and it is not manufuactured with top quality components.
Having said all that, you can still have lots of fun with them, and some shoot surprisingly very well (I saw a .223 version that was a sub .5MOA shooter!). The corollary is that some do not shoot that well. Tolerances of manufacturing mean some are better/worse than others.
If you want true precision accuracy, you will need to swap out a number of components to make that happen - or you can spend the money to achieve that right off the bat.