Fur could make cockney less cold (5)
I believe the answer is:
otter
I believe this is a double definition.
'fur' is the first definition.
(I know that otter is a type of fur)
'cockney less cold' is the second definition.
('hotter' - 'hot' can be the opposite of 'cold' so perhaps 'hotter' is reasonable for 'less cold' - said with a cockney accent, dropping the 'H')
'could make' acts as a link.
(Other definitions for otter that I've seen before include "Freshwater brown carnivore" , "bad-tempered little beast" , "carnivore is concerned" , "Riverine mammal" , "Holt dweller" .)