Perhaps pop star Dido cold at heart (4)
I believe the answer is:
idol
'perhaps pop star' is the definition.
'dido cold at heart' is the wordplay.
'dido' becomes 'id' (I can't explain this - if you can you should believe this answer much more).
'at heart' means to look at the middle letters.
The middle letters of 'cold' are 'ol'.
'id'+'ol'='IDOL'
Can you help me to learn more?
(Other definitions for idol that I've seen before include "Admired figure" , "Image of a god (not icon)" , "Hero, star" , "As before, fake" , "Billy" .)