How we may heat wine, we’re told — or fish (6)

I believe the answer is:

mullet

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'fish' is the definition.
(I know that mullet is a type of fish)

I don't understand the remainder of the clue.

(Other definitions for mullet that I've seen before include "Starfish" , "swimmer" , "Fish, male hairstyle" , "Food fish - hairstyle" , "Barnet?" .)

I've seen this clue in The Times.

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