Part of the reason for that has to do with the gas operation system the Mini 14 employs. It has a floating piston attached to a recoil arm that seats in a fixed gas cylinder inside the forend at the front of the stock. Gas is bleed off the barrel into the fixed cylinder and forces the floating piston out of the cylinder. When the hot gas vents into the forend it heats the underside of the barrel diferentially from the top of the barrel. That causes the barrel to "warp" slightly from the heat.
At close ranges, it means nothing. Out past 100 yards the warping causes the point of aim to shift as the weapon heats from use. This is bad for accuacy. The advantage of the system is that it works and it works all the time. After the weapon heats totally, the point of aim changes again. It can be annoying.
Ahh... excellent information you have there. I'm not too knowledgeable about semi-automatic rifles. All mine are bolt action hunting rifles.
I am in the market for a Springfield M1A soon. (civilian M-14) Such a nice rifle.
I think you described an M1A or M14. The gas cylinder has a gas pipe attached and it doesn't move. The operating rod has a block in the front that the pipe fits into. The gases push the operating rod to the rear. It has a spring return to chamber the round. The system is identical to the M1 Carbine. Heating is the problem as you mentioned but I also think Ruger makes horrible Mini barrels.
If you really want to see horrible groups, tighten those 10-32 screws on the gas cylinder.