Not hot on illness (4)
I believe the answer is:
cold
This clue is a double definition.
'not hot' is the first definition.
('cold' is the opposite to 'hot')
'illness' is the second definition.
(cold is a kind of illness)
'on' acts as a link.
(Other definitions for cold that I've seen before include "Lacking affection" , "Frigid" , "Chilly; minor ailment" , "Glacial" , "Lacking emotion" .)