If a person comes across to others as cold, aloof, or standoffish, what can he do to show his desire to be warm and approachable?
A person who seems to be "cold, aloof, or standoffish" can certainly change that impression--if he wants to, of course. There are certainly some people who do not want to engage with others in a social setting and use their body language to make sure everyone in the room knows it. Others give this impression but are really just shy and do not really know how to be more approachable; their aloofness is their self-defense.
In either case, the first thing a person whose body language says "stay away" must do is want to change the impression he is giving others.
Second, he must examine what he is doing to create this impression. A person emitting the "stay away" vibe is probably standing or sitting alone with his arms crossed and a serious (or even sour) look on his face. He must become aware of whatever he might be doing to seem unapproachable. This may just be a position of habit rather than intent, so to change the impression he must change his position.
Finally, he must make a conscious effort to change the way he appears to others. If he physically connects himself to a group, even if he does not know anyone or say anything, he will seem more sociable. If he listens and reacts to others, even if it is just through facial expression or laughter, he will seem more approachable. If he is able to demonstrate some kind of interest in whatever is being discussed or in someone he has never met, he will certainly not seem "cold, aloof, or standoffish." In fact, he will seem quite friendly and sociable.
In social situations, a person must simply decide that the occasion will not just be about him: his shyness, his grumpiness, his fears. The key to being approachable and friendly is the sincere desire to meet new people and learn new things--something which will inevitably happen if he spends time getting to know other people.
The eNotes link below is a great source for any further study of body language.