How could you manage you own/another person’s emotions to prevent them impacting the conflict?

Think of a conflict you have been part of, where you haven’t been willing to resolve it because of high emotions, or (if you prefer), reflect on a conflict where you have seen others be highly emotional.

Where do those emotions come from?
What are the benefits of having those emotions?
How could you manage you own/another person’s emotions to prevent them impacting the conflict?