Eavesdropper to run away if the heat's on? (6)

I believe the answer is:

icicle

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'eavesdropper' is the definition.
(an icicle might hang down from an eaves)

I cannot understand how the remainder of the clue works.

Can you help me to learn more?

(Other definitions for icicle that I've seen before include "this tapers" , "Suspended frozen water" , "Pendent spear of frozen water" , "Winter spike" , "Frozen water drip" .)

I've seen this clue in The Sun.

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