Crossword Genius

Not very hot, but nevertheless approved of (4)

Ross

I believe the answer is:

cool

I'm a little stuck... Click here to teach me more about this clue!

'not very hot' is the definition.
'cool' can be an answer for 'hot' (thesaurus). I am unsure of the 'not very' bit.

'nevertheless approved of' is the wordplay.
I cannot quite see how this works, but
'of' could be 'o' and 'o' is present in the answer.
The remaining letters 'col' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...

'but' acts as a link.

Can you help me to learn more?

(Other definitions for cool that I've seen before include "Fashionably attractive" , "Quite cold" , "Fan" , "Not keen!" , "chic" .)

I've seen this clue in the Evening Standard.
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