The most common and most likely answer to this crossword clue is the 8 letter word TESTIEST
I've seen this crossword clue in The Daily Telegraph
T
E
S
T
I
E
S
T
Buddy explains!

The straight part
We know that "most bad-tempered" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case most bad-tempered = testiest.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does TESTIEST mean?
TESTIEST adjective- Easily annoyed, irritable.
- Marked by impatience or ill humor.