Feel hot carrying heartless duke's cargo (6)
I believe the answer is:
burden
'cargo' is the definition.
(thesaurus)
'feel hot carrying heartless duke's' is the wordplay.
'feel hot' becomes 'burn' (eg a body part might burn or feel hot).
'carrying' means one lot of letters goes inside another.
'heartless' means to remove the middle letters.
'duke' with its centre removed is 'de'.
'burn' going around 'de' is 'BURDEN'.
(Other definitions for burden that I've seen before include "Oppressive duty" , "Onus or load" , "A heavy load or difficulty" , "Load or responsibility carried" , "Encumbrance" .)