Country doctor, one in remarkably cool area (8)
I believe the answer is:
colombia
'country' is the definition.
(Colombia is an example)
'doctor one in remarkably cool area' is the wordplay.
'doctor' becomes 'mb' (Bachelor of Medicine, Medicinae Baccalaureus**).
'one' becomes 'i' (Roman numeral).
'in' means one lot of letters goes inside another.
'remarkably' indicates anagramming the letters (I've seen this in other clues).
'area' becomes 'a' (maths abbreviation).
'mb'+'i'='mbi'
'cool'+'a'='coola'
'coola' is an anagram of 'coloa'.
'mbi' going within 'coloa' is 'COLOMBIA'.
(Other definitions for colombia that I've seen before include "S American state" , "Coffee-exporting South American country" , "Northwestern republic in South America" , "Bogot++ is its capital" , "South American Republic" .)