City hospital is cold, when toured by a dictator (3,9)
I believe the answer is:
san francisco
'city' is the definition.
(San Francisco is an example)
'hospital is cold when toured by a dictator' is the wordplay.
'hospital' becomes 'san' (I've seen this in other clues).
'cold' becomes 'c' (eg on taps).
'when toured by' is an insertion indicator.
'a dictator' becomes 'franco' (I've seen this before).
'is'+'c'='isc'
'isc' put within 'franco' is 'francisco'.
'san'+'francisco'='SAN FRANCISCO'
(Other definitions for san francisco that I've seen before include "US west coast port" , "City in California" , "hilly city" , "Californian port" , "Californian city" .)