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Cold affects the speed at which molecules are moving around. Fire is a phenomenon produced generally by exothermic chemical reactions between molecules. The part of the fire you see is, if I understand correctly, the photons emitted by excited electrons moving to a lower energy state after the reaction.

All other things being equal, the colder it is, the less the candidate molecules are moving, and thus the less likely they are to encounter each other and react. IIUC almost all chemical reactions are less vigorous at lower temperatures, disallowing convection of course.




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