mid-14c., "make (someone) ardent; set (the spirit, etc.) on fire" with a passion or religious virtue, a figurative sense, from Old French enflamer "catch fire; set on fire" (Modern French enflammer), from Latin inflammare "to set on fire, kindle," figuratively "to rouse, excite," from in- "in" (from PIE root *en "in") + flammare "to flame," from flamma "a flame" (see flame (n.)).
The literal sense of "to cause to burn" first recorded in English late 14c. Meaning "to heat, make hot, cause inflammation" is from 1520s. Formerly also enflame, but since 16c. the spelling with in- has predominated. Related: Inflamed; Inflaming.
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Harper, D. (n.d.). Etymology of enflame. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/enflame