The first half of your question seems less specifically related to music and more generally to the optimal state of activity Mihaly Csikszentmihalyi refers to as "Flow":
The best moments in our lives are not the passive, receptive, relaxing times… The best moments usually occur if a person’s body or mind is stretched to its limits in a voluntary effort to accomplish something difficult and worthwhile.
His wikipedia page describes the general nature of flow:
Csikszentmihályi characterized nine component states of achieving flow including "challenge-skill balance, merging of action and awareness, clarity of goals, immediate and unambiguous feedback, concentration on the task at hand, paradox of control, transformation of time, loss of self-consciousness, and autotelic experience". To achieve a flow state, a balance must be struck between the challenge of the task and the skill of the performer. If the task is too easy or too difficult, flow cannot occur. Both skill level and challenge level must be matched and high; if skill and challenge are low and matched, then apathy results.
You should check out some of his books, they're an interesting read, and it might help you discover how to achieve flow more frequently while playing.
In terms of warm-up and actual exercises to get yourself "warmed up", well there's a ton of different answers. Personally, I've found that using a rough estimate of Mihaly's formula to guide myself into a state of pure focus helps a lot- that is, if you want to feel like you're completely immersed in the activity, determine what your skill level is and match it with something that's challenging for you to be completely engrossed, but not so challenging that it's frustrating for you to feel like you're performing well.