A foreign, well-liked metropolis, needs no introduction in a state that's not hot (12)
I believe the answer is:
unpopularity
'no introduction in a state that's not hot' is the definition.
I can't tell whether this defines the answer.
'a foreign well-liked metropolis' is the wordplay.
'a foreign' becomes 'un' ('a' translated into French).
'well liked' becomes 'popular' (I've seen this before).
'metropolis' becomes 'ity' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'un'+'popular'+'ity'='UNPOPULARITY'
'needs' is the link.
Can you help me to learn more?
(Other definitions for unpopularity that I've seen before include "Great lack of appeal" , "Lack of mass appeal" .)