Crossword Genius

How one might deny being frigid? (5)

Ross

I believe the answer is:

hotly

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'how' is the definition.
Both the answer and definition are adverbs. Perhaps you can see a link between them that I can't see?

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(Other definitions for hotly that I've seen before include "showing passion" , "showing eagerness" , "disputed thus?" , "With zeal - as one may be pursued" , "in an ardent manner" .)

I've seen this clue in the Evening Standard.
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