Cold-hearted but getting better (5)
I believe the answer is:
nicer
'better' is the definition.
(I've seen this before)
'cold-hearted but' is the wordplay.
'cold' becomes 'ice' (I've seen this before).
'hearted' is an insertion indicator (some letters go to the heart of the word).
'but' becomes 'nr' (I can't explain this - if you can you should believe this answer much more).
'ice' placed within 'nr' is 'NICER'.
'getting' is the link.
Can you help me to learn more?
(Other definitions for nicer that I've seen before include "relatively pleasant" , "More pleasant or courteous" , "Even more 7 down!" , "improved" , "Pleasanter" .)