Temperature lowered initially in America's city (5)
I believe the answer is:
tulsa
'city' is the definition.
(Tulsa is an example)
'temperature lowered initially in america's' is the wordplay.
'temperature' becomes 't' (abbreviation).
'initially' suggests taking the first letters.
'in' indicates putting letters inside.
'america' becomes 'usa' (United States of America).
The first letter of 'lowered' is 'l'.
'l' inserted into 'usa' is 'ulsa'.
't'+'ulsa'='TULSA'
(Other definitions for tulsa that I've seen before include "A lust for the Oklahoma oil city?" , "Oklahoma city (only 24 hours away?)" , "An OK place" , "Oklahoma river port" , "Twenty-four Hours from - (Gene Pitney)" .)