Heat can 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.
'run' becomes 'r' (cricket abbreviation).
'grim' becomes 'dour' (synonyms).
'a'+'r'+'dour'='ARDOUR'
'can make' is the link.
(Other definitions for ardour that I've seen before include "Burning desire" , "Emotional warmth" , "Passionate warmth" , "Love, passion" , "Fervour, zeal" .)