Warm through hearts and dine (4)
I believe the answer is:
heat
'warm' is the definition.
(thesaurus)
'hearts and dine' is the wordplay.
'hearts' becomes 'h' (abbreviation used in card games e.g. bridge).
'and' is a charade indicator (letters next to each other).
'dine' becomes 'eat' (eat a meal).
'h'+'eat'='HEAT'
'through' is the link.
(Other definitions for heat that I've seen before include "It's measured in therms" , "Warm up" , "Hotness" , "Toast" , "eliminating round" .)