Temperature was rising for antelopes in desolate areas (10)
I believe the answer is:
wastelands
'desolate areas' is the definition.
(a wasteland is a desolate region)
'temperature was rising for antelopes' is the wordplay.
'temperature' becomes 't' (abbreviation).
'was' becomes 'saw' (I am not sure about this - if you are sure you should believe this answer much more).
'rising' is a reversal indicator (going up in a down clue).
'for' is a charade indicator (letters next to each other).
'antelopes' becomes 'elands' (type of antelope).
't'+'saw'='tsaw'
'tsaw' back-to-front is 'wast'.
'wast'+'elands'='WASTELANDS'
'in' is the link.
(Other definitions for wastelands that I've seen before include "wilderness" , "Deserts" .)