Cold friend's wrapped in warm material (10)
I believe the answer is:
chinchilla
'warm material' is the definition.
(chinchilla fur)
'cold friend's wrapped' is the wordplay.
'cold' becomes 'chill' (chill is a kind of cold).
'friend' becomes 'china' (cockney rhyming slang, mate is china plate).
'wrapped' indicates putting letters inside.
'chill' placed within 'china' is 'CHINCHILLA'.
'in' acts as a link.
(Other definitions for chinchilla that I've seen before include "(Fur of) a small South American rodent" , "Soft grey fur" , "Rabbit" , "little furry animal" , "furry creature" .)