Cool show on TV leading to complaint (3-9)

I believe the answer is:

air-condition

'cool' is the definition.
(thesaurus)

'show on tv leading to complaint' is the wordplay.
I cannot quite see how this works, but
'show' could be 'air' (both can mean broadcast) and 'air' is found within the answer.
'on' is within the answer.
This explanation may well be incorrect...

I've seen this clue in The Times.

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