Hot realm is properly marked by equality of temperature (10)
I believe the answer is:
isothermal
'hot realm is properly marked by equality of temperature' is the definition.
I can't judge whether this defines the answer.
'hot realm is properly marked by' is the wordplay.
'hot' is an anagram indicator (letters heated up or stimulated into a new order).
'properly marked' becomes 'oth' (I can't explain this - if you can you should give a lot more credence to this answer).
'by' says to put letters next to each other.
'realm' anagrammed gives 'ermal'.
'is'+'oth'='isoth'
'ermal' put after 'isoth' is 'ISOTHERMAL'.
Can you help me to learn more?
(Other definitions for isothermal that I've seen before include "at constant temperature" , "without change in temperature?" .)