There is no free ride. If ya want a lighter gun, it's gonna kick more. If the lighter gun is light, because the barrel is thinner, then that barrel will very likely heat up faster than a heavier barrel.
I've owned a number of Ruger Compacts, and Ultra Lights. I did not buy any of them with the intention of making them red hot by shooting long strings at the range. I bought them to carry hunting, and they do a great job of that. My most recent Ultra Light, in .30-06, shoots less than 1-1/2" groups at the range, shooting 3 or 5 shot groups. I will never try seeing how many shots I have to shoot to heat it up, and seriously affect accuracy.
And, +1+ for the Compact, in 7mm/08. Everything else being equal, that 7-08 is a very easy shooting cartridge, in any rifle. And the Compact, is not marketed as shorter, just to satisfy smaller people. It's short, to make it handle very well, in hunting situations. It does a great job.
WAYNO.