Is there a word to describe the feeling of heated argument?

This is tricky as you're more centric on feeling to go into a heated argument whether against or defend.

So, we almost have some related single-words which best describe however as per me, it is :

opinionated : believing very strongly and conveying it

If you are opinionated, you obstinately hold on to your opinions, and you don't hesitate to let other people know what those opinions are.

That is , opinionated person will step in and start saying something or even defend about something when people points it out. (from Question).

So willingly one is ready to go into any level of arguement to make his/her opinion count.

Moreover, even in your couple example I believe opinionated fits as one of the two went in to heated discussion when they had this feeling to defend or to argue and that feeling borns when you want your opinion to be counted.

Nevertheless, I'd like to share more related words with their meaning & example sentence, like :

Pugnacious : Combative in nature; ready to fight

take this example : The pugnacious little boy constantly talks back to his mother.

argumentative : (adj.) wanting to quarrel

Eg : The law students were an unusually argumentative group.

Hope this helps.