Cooler adherent (3)
I believe the answer is:
fan
I believe this clue is a double definition.
'cooler' is the first definition.
(something which cools)
'adherent' is the second definition.
(thesaurus)
(Other definitions for fan that I've seen before include "Cool - enthusiast" , "Cooling device or disciple of performer" , "Lady Windermere's - -" , "Spanish women wave it to cool themselves" , "Keen follower; cooler" .)