Country not warm by the sound of it (5)
I believe the answer is:
chile
'country' is the definition.
(Chile is a country)
'not warm by the sound of it' is the wordplay.
'not warm' becomes 'chilly' (I've seen this before).
'by the sound of it' shows a homophone (sound like).
'chilly' sounds like 'CHILE'.
(Other definitions for chile that I've seen before include "Long, thin country" , "Most southerly American country" , "Long narrow country" , "S American country, capital Santiago 95)" , "Country liberated by Bernardo O'Higgins" .)