The most common and most likely answer to this crossword clue is the 12 letter word UNRESPONSIVE
I've seen this crossword clue in The Daily Telegraph
U
N
R
E
S
P
O
N
S
I
V
E
Buddy explains!
The straight part
We know that "Cool" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cool = unresponsive.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 UNRESPONSIVE mean?
UNRESPONSIVE adjective- Not responsive; unreactive.
- Indifferent or apathetic; emotionless.