Hmm, that is not what I am experiencing.

I have about 8 Savage rifles and when I take one to the range, I shoot between 75 and 100 rounds with the rifles I brought.
I only notice a drop in POI after a rifle barrel heats up to over 113 to 122 degrees F..
I have LCD temperature strips mounted on each barrel so I can keep track of temperature.
As long as I keep the barrel within 86 to 110 degrees F, most of my Savages are tack drivers.

On hot summer days, temperatures rise pretty quickly so I get to shoot only 5 or 6 shots before I have to let the barrels cool.
I switch to a different rifle while I let a barrel cooling fan get the temperature down.
On cold winter mornings with temperatures in the low to mid 20s, I can shoot 15 to 25 shots before the barrel gets too hot depending upon how cold it starts.
Of course, once the barrel cools down below 86 degrees, I start up again and find that I get more like 12 shots before I have to stop again.

When the barrels heat up past 110 to 113, I find the POI on my most accurate rifles drop about 1/4 inch but the accuracy remains.
I haven't noticed a growth in average group size, only a shift in POI.

I clean and decopper the barrels after every range session.