Heat that could make a run grim (6)
I believe the answer is:
ardour
'heat' is the definition.
(I've seen this before)
'a run grim' is the wordplay.
'a run' becomes 'ar' (I've seen this in other clues).
'grim' becomes 'dour' (synonyms).
'ar'+'dour'='ARDOUR'
'that could make' is the link.
(Other definitions for ardour that I've seen before include "Love and enthusiasm" , "Emotional warmth" , "Burning desire" , "Passion, rapture" , "Fervour, zeal" .)