WV,
The phenomenon that makes your rifle shoot more precisely as the barrel heats-up after a few shots is "thermal dimensional stabilization". In plain English, when a barrel is machined and rifled at the factory, some localized heating will always occur. Heat can be minimized by abundant use of cutting fluid and machining using very shallow cuts per pass.
When machining is aggressive or not enough coolant is used, residual stresses from the heat generated by friction from machining/rifling operations are induced in the steel. As the barrel cools down and the barrel contracts, there will be some very slight deformation of the bore diameter along the barrel's axis, due to these residual stresses.
When you shoot the first 3 or 4 rounds from a cold barrel, the heat from the burning powder is absorbed by the barrel, causing it to expand. As the barrel expands, the small amount of deformation that resulted from the residual stresses from machining is countered, eliminating the distortion, thus making the barrel more dimensianally uniform, which is why, in your rifle's case, better groups are produced with a warm barrel.
The key to maintaining good dimensions on machined products lies mostly in heat management. Aggressive machining produces more heat from friction. Relatively fast speeds, very shallow cuts and abundant cooling/cutting fluid flow will result in less residual stresses and tighter tolerances. Stress relieving by placing the machined barrel in an oven for a few hours at moderate temperature before drilling or rifling will also help. Some barrel makers stress-relieve their barrels after rifling them, prior to lapping.
I hope this helps to explain what you are observing
