noun
violent temper; termagancy
Describes a fierce, hot-tempered, or quarrelsome personality, often associated with a rough or aggressive disposition. The term is somewhat literary and not extremely common in everyday conversation.
彼の鉄火肌には誰も手を焼いている。
Everyone is at their wits' end with his violent temper.
あの人の鉄火肌は、時として周囲を困らせる。
That person's termagancy sometimes troubles those around them.
短気 means short-tempered or quick to anger, but 鉄火肌 carries a stronger nuance of a rough, aggressive, and quarrelsome personality.
The exact derivation is uncertain. The kanji 鉄火 (iron and fire) suggest a fierce, fiery nature, and 肌 (skin) metaphorically refers to one's disposition or temperament.