In any conversation during which the temperature has started to rise, wait 10 seconds before you respond. That's it. Just stop. Don't respond immediately. Instead, wait and give yourself a moment to be intentional in your response, instead of emotional. It isn't magic, but you might be surprised at how well it works.
If leadership is mostly about influence--and it is--then the ability to communicate a vision and motivate people to move toward that vision is the single most important characteristic a leader can have.