Crossword Genius

A politician with impact, warmth, referring to arena for plays (12)

Ross

I believe the answer is:

amphitheatre

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'referring to arena for plays' is the definition.
I can't tell whether this definition defines the answer.

'a politician with impact warmth' is the wordplay.
'a' becomes 'amp' (A is the symbol for the amp or ampere).
'politician' becomes 're' (I can't explain this - if you can you should believe this answer much more).
'with' means one lot of letters go next to another.
'impact' becomes 'hit' (hitting is a kind of impacting).
'warmth' becomes 'heat' (synonyms).
'hit'+'heat'='hitheat'
're' after 'hitheat' is 'hitheatre'.
'amp'+'hitheatre'='AMPHITHEATRE'

Can you help me to learn more?

(Other definitions for amphitheatre that I've seen before include "Arena; gallery tier" , "Large oval stadium with tiers of seats" , "Theatre gallery seating area" , "Classical performance area" , "Classical home for drama" .)

I've seen this clue in The Times.
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