Heaters working in May, perhaps (7)
I believe the answer is:
theresa
'may perhaps' is the definition.
(Theresa May, former UK prime minister)
'heaters working' is the wordplay.
'working' is an anagram indicator.
'heaters' is an anagram of 'THERESA'.
'in' is the link.
(Other definitions for theresa that I've seen before include "Woman" , "May's one" , "Maria --, Austrian ruler" , "-- May, MP" , "Lisieux saint" .)