I don't wait until after an altercation to calm down. The moment I realize that things are getting heated, I excuse myself from the conversation and let the other person know I'll talk more when I'm calmer. It might take a few minutes, a couple hours, or even a few days until I'm completely ready to talk. By the time I do, I've thoroughly digested the other person's viewpoint and figured out how to present my side of things in a way that honors their position, too.
If I can't find a way to honor theirs, I make a decision about whether to surrender altogether (some arguments aren't worth it), or I have a plan for what I will do if they don't see my viewpoint at all, and it'll be something that they cannot prevent me from executing but that was planned with them in mind in some way.