Conclude with a short number that's hot (7)

I believe the answer is:

inferno

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'that's hot' is the definition.
I can't judge whether this defines the answer.

'conclude with a short number' is the wordplay.
'conclude' becomes 'infer' (inferring is a kind of concluding).
'with' is a charade indicator (letters next to each other).
'a short number' becomes 'no' (abbreviation for 'number'; 'short' asks for a short form).
'infer'+'no'='INFERNO'

Can you help me to learn more?

(Other definitions for inferno that I've seen before include "(Fiery) Hell" , "Hellish poem" , "Dante's Hell" , "Terrible fire" , "Uncontrollable fire" .)

I've seen this clue in The Irish News.

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