"That person is very ill-tempered"; He/she is Ill-tempered" — These examples all imply a "negative" personality trait. Fiery tempered, or quick-tempered, doesn't always imply a negative personality. A girl can have a fiery-temper, which means that maybe she is quick to fight or get angry, but that quality might be something that is well liked about her. EX: "That new red-head in class has a fiery-temper! It's so attractive!" red-head (a person, usually a female, with naturally red hair) ("fiery red-head" is a common expression; to be called a fiery red-head is a good thing. It implies that her personality is attractive) "Her quick temper is what I like about her! I think it is so alluring." "Do you know Bob? He is a really ill-tempered person. I hate to be around him." "Does Robert have to come? He is so ill-tempered! He always ruins the party!" "Short-tempered"; "has a short fuse" can be interchangeable with ill-tempered, and keep the same meaning.

Fiery can be used in some phrases to mean a personality that can be easily angered or excited, but it is not a bad thing - it is just who they are. For some reason if you have this quality and you have red hair, you are called a fiery red-head. But the term fiery does not go with other color hair, and the quality is not as forgiven/overlooked with other color hair. Other phrases are fiery attitude - temper - personality - spirit. The term is for women usually. In all these cases, like read-head, the person is being given a pass for their temper. It is also being dismissive of the persons concerns. It is like saying "don't worry about what she is upset about - she is always upset - we like that about her."... Totally taking the attention away from her concern and focusing on the attitude and person with the ignored concerns.

I would say 'he/she is quick-tempered'.

"Ill tempered" is more common to use and people will understand straight away. If you are looking for more fancy word similar to "Ill tempered", you can say "he/she has a short fuse".