Get more intense (6)
(Other definitions for deepen that I've seen before include "Get stronger" , "Make stronger" , "make room for more water" , "Dig out" , "Make (colour) darker" .)
'get more intense' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for heat up that I've seen before include "Make more intense" , "Warm through" .)