Small Channel Islands firm - with my backing - imported heater from Africa (8)
I believe the answer is:
scirocco
'imported heater from africa' is the definition.
(hot wind blowing from North Africa)
'small channel islands firm with my backing' is the wordplay.
'small' becomes 's' (abbreviation - e.g. clothes size).
'channel islands' becomes 'CI'.
'firm with' becomes 'oc' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'my' becomes 'cor' (both are expressions of surprise).
'backing' is a reversal indicator.
'oc'+'cor'='occor'
'occor' reversed gives 'rocco'.
's'+'ci'+'rocco'='SCIROCCO'
(Another definition for scirocco that I've seen is " Dry hot dusty wind blowing from N Africa".)