Small stream not enough for poet (4)

I believe the answer is:

burn

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'small stream' is the definition.
(I've seen this before)

I can't explain the rest of the clue.

(Other definitions for burn that I've seen before include "Combust" , "running water" , "pain during exercise" , "Feel hot, small stream" , "Set 1 across [ALIGHT]" .)

I've seen this clue in The Guardian.

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