Lover is cooler (3)
I believe the answer is:
fan
This clue is a double definition.
'lover' is the first definition.
(synonyms)
'cooler' is the second definition.
(something which cools)
'is' is the link.
(Other definitions for fan that I've seen before include "Cooling device for devoted follower?" , "Aficionado" , "Great enthusiast" , "Manual cooling device - for admirer?" , "Enthusiastic admirer as of pop star" .)