The most common and most likely answer to this crossword clue is the 4 plus 4 letter word TONE DOWN
I've seen this crossword clue in Financial Times
T
O
N
E
D
O
W
N
More clues leading to the result TONE DOWN
- First day in shopping centre gives you temper
- Simplify a couple of clues before complaint finally begins
- Mute individual welcomed finally into community
- Reduce intensity? No we don’t, unfortunately
- Dull, like a very flat note?
- Beginning to tackle crossword clue in temper
- The third to rate this clue as “moderate”
- Moderate carapace supporting tons?
- Moderate D to C, perhaps?
- Moderate, taking time, the 17th clue
Buddy explains!

The straight part
We know that "temper" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case temper = tone down.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.