Crossword Genius

What warms big building on Broadway initially lacking temperature (6)

Ross

I believe the answer is:

heater

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'what warms' is the definition.
(heaters warm things)

'big building on broadway initially lacking temperature' is the wordplay.
'big building on broadway' becomes 'ter' (I can't justify this - if you can you should give a lot more credence to this answer).
'initially' says to put letters next to each other.
'lacking' means to remove the last letter (the word is incomplete or lacking).
'temperature' becomes 'heat' (heat is a kind of temperature).
'heat' with its final letter taken away is 'hea'.
'ter' after 'hea' is 'HEATER'.

Can you help me to learn more?

(Other definitions for heater that I've seen before include "Source of warmth; gun" , "Room warmer" , "Warming device" , "fire" , "Radiator" .)

I've seen this clue in The Times.
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