Is there a word for "not thinking clearly because of anger"?

For example: two are arguing and one makes a personal attack. They both become angry causing neither to speak reasonably.

Any word for this?

EDIT: In my example, instead of 'angry', I should have used the word 'indignant'. I wasn't looking for extremes, like 'seeing red' or 'blinded by rage'.

I also find 'enraged', 'infuriated', and 'apoplectic' not suitable. I'm looking for "a state of irrationality, caused by indignation."

From the responses so far, I think the best expression is "Their judgment became clouded by indignation."

Solution 1:

The were enraged and apoplectic and no doubt synonyms of those, leading them to say things "in a rage" or if really extreme while "seeing the red mist".

Solution 2:

How about berserk:

Out of control with anger or excitement; wild or frenzied

Solution 3:

The expression blinded by rage may suggest the idea of being unable to think and behave reasonably because of anger. Also mad with rage.

Solution 4:

Enraged, blinded by rage, furious all suggest losing clarity of mind. The British also use a colloquial fuming as adjective to describe that same state of mind.

Solution 5:

Normally sane people might do something unwise in the heat of the moment:

if you say or do something in the heat of the moment, you say or do it without thinking because you are angry or excited Frank doesn't hate you. He just said that in the heat of the moment.