Turn down in cold brief message (7)

I believe the answer is:

incline

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'turn down' is the definition.
'incline' can be an answer for 'turn' (I've seen this before). I'm not sure about the 'down' bit.

'in cold brief message' is the wordplay.
'cold brief message' becomes 'cline' (I can't explain this - if you can you should believe this answer much more).
'in'+'cline'='INCLINE'

Can you help me to learn more?

(Other definitions for incline that I've seen before include "Have tendency or slope" , "lean forward" , "Gradient" , "tip" , "prejudice" .)

I've seen this clue in the Sydney Morning Herald.

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