Not okay being warm, possibly? (6)

I believe the answer is:

uncool

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'warm possibly?' is the definition.
'uncool' can be an answer for 'warm' (I've seen this before). I am not sure about the 'possibly?' bit.

'not okay' is the wordplay.
'not' becomes 'un' (prefix meaning 'not').
'okay' becomes 'cool' ().
'un'+'cool'='UNCOOL'

'being' is the link.

Can you help me to learn more?

(Other definitions for uncool that I've seen before include "Not fashionable (colloq.)" , "Not with it (but warm?)" , "hot?" , "Not in fashion or with it" , "Old-fashioned" .)

I've seen this clue in The Telegraph.

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