At home, cool temperature delivers baby (6)
I believe the answer is:
infant
'baby' is the definition.
('infant' can be a synonym of 'baby')
'at home cool temperature' is the wordplay.
'at home' becomes 'in' ('in' can be similar in meaning to 'at home').
'cool' becomes 'fan' (I've seen this in other clues).
'temperature' becomes 't' (abbreviation).
'in'+'fan'+'t'='INFANT'
'delivers' acts as a link.
(Other definitions for infant that I've seen before include "Small baby" , "Small boy" , "Toddler" , "Rudimentary" , "Youngster" .)