A .75" group including a cold bore shot isnt bad. For big game it is plenty suitable. I have had rifles that had cold bore issues. They were however concistent in their cold bore bullet placements. I learned where the cold bore shot landed and simply compensated for it. It is a very common issue. I say issue because it is hardly a problem. I am fortunate enough to have 2 primary rifles that do not have cold bore issues even down to the 0 degree F. mark. Your issues may be fixed by applying what others have stated. If they are not, this is where knowing your rifle pays off. It may be another thing you have to factor in for the shot, but a very minimal one at that.
Long range shooting is a process that ends with a result. Once you start to focus on the result (how bad your last shot was, how big the group is going to be, what your buck will score, what your match score is, what place you are in...) then you loose the capacity to focus on the process.