It's not quite so hot in this part of London (4)
I believe the answer is:
soho
'this part of london' is the definition.
(district of Westminster)
'it's not quite so hot' is the wordplay.
'it's not quite' means to remove the last letter (most but not all of the word).
'so'+'hot'='sohot'
'sohot' with its last letter taken off is 'SOHO'.
'in' acts as a link.
(Other definitions for soho that I've seen before include "W London area" , "Theatre and night-life district of London" , "Once notorious part of central London" , "London night life area" , "London's former Bohemia" .)