Mineral associated with cold heart (4)
I believe the answer is:
core
'heart' is the definition.
(I know that heart can be written as core)
'mineral associated with cold' is the wordplay.
'mineral' becomes 'ore' (ore is a kind of mineral).
'associated with' says to put letters next to each other.
'cold' becomes 'c' (eg on taps).
'ore' put after 'c' is 'CORE'.
(Other definitions for core that I've seen before include "Drilled rock sample" , "Central or most important part of something" , "The centre part, as of an apple" , "Inmost part" , "Kernel" .)