You can prepare an agenda for your follow-up or craft a statement of facts or beliefs that frame your side of the argument. Both of you should do this and share it with the other to review in advance. This avoids possible inflammatory statements at the moment and forces you to think about the other person's position.

Overall, it's best to defuse these situations quickly and let the other person know you have no interest in conflict, but that you'd much rather listen, share, and come to an understanding calmly. It's the only way forward -- for the issue at hand and for your relationship.