The powers that be have run hot bath (5)
I believe the answer is:
therm
'hot bath' is the definition.
(historical term for a public bath)
'the powers that be have run' is the wordplay.
'the powers that be' becomes 'them' ('them' can mean unspecified powerful forces).
'have' is an insertion indicator.
'run' becomes 'r' (cricket abbreviation).
'them' enclosing 'r' is 'THERM'.
(Other definitions for therm that I've seen before include "Unit of heat energy" , "Unit of heat and gas measure" , "Unit of heat as in gas supply" , "it measures heat" , "Amount of heat" .)