Bill's in bed - rising temperature (4)
I believe the answer is:
debt
'bill's' is the definition.
(thesaurus)
'bed rising temperature' is the wordplay.
'rising' says the letters should be written in reverse (going up in a down clue).
'temperature' becomes 't' (abbreviation).
'bed' backwards is 'deb'.
'deb'+'t'='DEBT'
'in' acts as a link.
(Other definitions for debt that I've seen before include "Amount owing" , "state of obligation" , "Financial problem?" , "Commitment" , "What's due" .)