Increase in temperature in inadequate rough hut (6)
I believe the answer is:
shanty
'rough hut' is the definition.
(shanty can mean a hut or shack)
I don't understand how the rest of the clue works.
(Other definitions for shanty that I've seen before include "Poor home - sailors' song" , "folk song" , "sea air" , "A traditional sailors' ballad" , "A sailor's traditional song" .)