The first thing you need do is clean the barrel - the foaming cleaners work well to help remove copper fouling, so does Windex with ammonia or a 50/50 ammonia/water mix - keep at it until the patches stop turning blue, then the copper fouling will be gone.
You also mentioned that the barrel heats up pretty quickly after 3-4 shots.... does this have anything to do with its poor groups - oh yeah, sure does.
Those rifles do not respond well to rapid (continued or sustained) fire. Every time I have shot one too quickly and heated the barrel, the groups open up. These are not military actions and barrels, they are light weight sporter set-ups that can and will heat up quickly with rapid fire and can even seize up on you if you pound them too hard for too long. They are lightweight actions and barrels so as to be carried easily and the thin tapered barrels will heat up quickly after 3-4 shots if you pound the shots out. If you want to see how it groups, fire one round per minute for a 3 shot group, let cool for 5 minutes and repeat, but let the barrel cool down before shooting again.
Your problem is not specific to the 760. Many shooters who purchase light weight bolt rifles, experience groups that open right up when they pound the rounds out. Even if you think you are taking your time and treating the old gal right, you may need to slow it down a bit. Try the first two shots from a cold barrel and see how she groups then, you might hopefully be surprised.