Hot, horribly lost, occasionally mean (6)
I believe the answer is:
stolen
'hot' is the definition.
(eg stolen goods are 'hot')
'horribly lost occasionally mean' is the wordplay.
'horribly' indicates anagramming the letters (a horribly wrong version of the letters).
'occasionally' indicates alternate letters (letters taken at regular intervals or occasions).
The alternating letters of 'mean' are 'en'.
'lost' with letters rearranged gives 'stol'.
'stol'+'en'='STOLEN'
(Other definitions for stolen that I've seen before include "Nicked" , "Taken unlawfully" , "Goods that have been taken dishonestly" , "Pilfered" , "subject to plagiarism" .)