late 13c., "to cook by dry heat," from Old French rostir "to roast, burn" (Modern French rôtir), from Frankish *hraustjan (cf. Old High German rosten, German rösten, Middle Dutch roosten "to roast"), originally "cook on a grate or gridiron," related to Germanic words meaning "gridiron, grate;" cf. German Rost, Middle Dutch roost.
Intransitive sense "be very hot, be exposed to great heat" is from c.1300. The meaning "make fun of in an affectionate way" is from 1710. From the same source as roster. Related: Roasted; roasting. Roast beef first recorded 1630s (cf. French rosbif, from English).