Sometimes, things don’t seem to calm down on their own, and some sort of intervention is clearly needed.
If you’re fairly in tune with your colleagues and can pinpoint a relevant segue, jump on that chance. You’ll help get the discussion back on track and help save your colleagues from saying something they might regret.

Evasive Maneuvers

When you feel a conversation heating up—fast—it’s probably time to step in and help mediate.  Pay close attention to the argument, and try to find some common ground between the two (or more) battling it out. If you can’t find anything, then come up with a suggestion of your own.  Try to ease the tension, not add fuel to the fire.

Mediate

Sometimes things get heated in the office, and people lose their temper. It happens when people are working hard and trying to do their best. 
If you trust your team and know your colleagues well enough to recognize something as just out of character, it might be best to just let it blow over before addressing it any further.

Ignorance is Bliss

You know what they say about tension; that when it's thick, you could cut it with a knife. It's uncomfortable enough to deal with this kind of situation in social situations, but add that kind of tension to a work environment, and you have a whole new level of awkwardness on your hands.