c. 1300, chaufen, "be provoked, grow or be excited;" late 14c. in literal sense "to make warm, to heat" (also intransitive, "to grow warm or hot"), especially (early 15c.) "to warm by rubbing, excite heat by friction," from Old French chaufer "heat, warm up, become warm" (12c., Modern French chauffer), from Vulgar Latin *calefare, from Latin calefacere "to make hot, make warm," from calere "be warm" (from PIE root *kele- (1) "warm") + facere "to make, do" (from PIE root *dhe- "to set, put").
From 1520s as "abrade the skin by rubbing." Figurative senses from late 14c. include now-obsolete "kindle (joy), inspire, make passionate" as well as "provoke, vex, anger." Related: Chafed; chafing. Chafing-dish is from late 15c.