I don't really see himas the "heart" of the group. And being emotional isn't always positive.
Sorry missed these quotes but I want to respond. No being emotional is definitely not always positive, but either is being logical. That is the point of Spock and Bones. Neither logic or emotion by themselves is enough you need both.
As for being the "heart" of the trio well I will stick with that.
Kirk is the man of action, the one who ultimately makes the decisions, or the body and soul of the group.
Spock is the mind. He helps Kirk with his decisions by giving him the logical, rational, and intelligent advice. McCoy is the heart by giving Kirk the humanistic and emotional advice. But again Kirk needed both sides.
Or you can just say they are Ethos, Pathos and Logos