Shut up keeping warmth in cover (6)
I believe the answer is:
sheath
'cover' is the definition.
(sheath is a kind of cover)
'shut up keeping warmth' is the wordplay.
'shut up' becomes 'sh'.
'keeping' means one lot of letters goes inside another.
'warmth' becomes 'heat' ('heat' can be a synonym of 'warmth').
'sh' enclosing 'heat' is 'SHEATH'.
'in' is the link.
(Other definitions for sheath that I've seen before include "Scabbard" , "cocktail dress" , "Condom" , "Protective cover" , "Protective covering for a knife" .)