Cycled round hot southern Aegean island (6)
I believe the answer is:
rhodes
'aegean island' is the definition.
(I've seen this before)
'cycled round hot southern' is the wordplay.
'cycled' becomes 'rode' (I've seen this in other clues).
'round' means one lot of letters goes inside another.
'hot' becomes 'h'.
'southern' becomes 's' (abbreviation).
'rode' enclosing 'h' is 'rhode'.
'rhode'+'s'='RHODES'
(Other definitions for rhodes that I've seen before include "British financier and coloniser in southern Africa, d. 1902" , "Colonial businessman" , "British imperialist; Greek island" , "Greek island - British-born South African statesman" , "Hordes go to the Greek island" .)