Hot and bothered, hates carrying the case (6)
I believe the answer is:
sheath
'the case' is the definition.
('sheath' can be a synonym of 'case')
'hot and bothered hates' is the wordplay.
'hot' becomes 'h' (abbreviation eg on taps).
'and' is a charade indicator (letters next to each other).
'bothered' indicates anagramming the letters.
'hates' is an anagram of 'sheat'.
'h' put after 'sheat' is 'SHEATH'.
'carrying' acts as a link.
(Other definitions for sheath that I've seen before include "Protective case for a knife or sword" , "Cover for a knife" , "Cover protecting" , "Close fitting dress" , "Blade-cover" .)