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1650s, alteration of simperen "to simmer" (late 15c.), possibly imitative; not thought to be connected to simper (v.). OED says the change is "probably due to a feeling of phonetic appropriateness." Figurative sense, of feelings, "to be agitated" is from 1764. Opposite sense, in simmer down, first recorded 1871, probably from the notion of moving from a full boil to a mere simmer.
I must and will keep shady and quiet till Bret Harte simmers down a little. [Mark Twain, letter, 1871]Related: Simmered; simmering. The noun meaning "a condition of simmering" is from 1809.