In cooler temperature delivers baby (6)
I believe the answer is:
infant
'baby' is the definition.
('infant' can be a synonym of 'baby')
'in cooler temperature' is the wordplay.
'cooler' becomes 'fan' (I've seen this before).
'temperature' becomes 't' (abbreviation).
'in'+'fan'+'t'='INFANT'
'delivers' is the link.
(Other definitions for infant that I've seen before include "Youngster" , "Very young child or baby" , "Small baby" , "Thing in early stage; minor (legal)" , "Tiny baby" .)