We've all felt states of mind where we might not be totally rational. If someone makes you angry, really angry, you start thinking more violent, non-productive things. Maybe you want to punch someone, but that's an irrational thought because it wouldn't accomplish anything. In that way, you could consider it to be madness.
I don't think that anger is momentary madness. Everyone experiences moments of frustration and despair that can cause them to act angry, but I don't think it is grounds to madness. I believe that madness is a clinical condition and there is a psychological damage to an individual in order for them to be diagnosed with madness.