Crossword Genius

One floored by warmth showing passion right through embrace (9)

Ross

I believe the answer is:

hearthrug

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'one floored by warmth' is the definition.
Although both the answer and definition are singular nouns, I cannot understand how one could define the other.

'showing passion right through embrace' is the wordplay.
'showing passion' becomes 'heart' (I can't explain this - if you can you should believe this answer much more).
'right' becomes 'r' (common abbreviation).
'through' indicates putting letters inside (inserted letters go through the word).
'embrace' becomes 'hug' (synonyms).
'r' placed within 'hug' is 'hrug'.
'heart'+'hrug'='HEARTHRUG'

Can you help me to learn more?

(Other definitions for hearthrug that I've seen before include "one's position's under fire" , "One floored by blaze" , "Mat near fire" , "Carpet in front of fire" , "floor-covering" .)

I've seen this clue in The Times.
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