melt (n.) Look up melt at Dictionary.com
1854, "molten metal," from melt (v.). In reference to a type of sandwich topped by melted cheese, 1980, American English.
melt (v.) Look up melt at Dictionary.com
Old English meltan "become liquid, consume by fire, burn up" (class III strong verb; past tense mealt, past participle molten), from Proto-Germanic *meltanan; fused with Old English gemæltan (Anglian), gemyltan (West Saxon) "make liquid," from Proto-Germanic *gamaltijan (source also of Old Norse melta "to digest"), both from PIE *meldh- (source also of Sanskrit mrduh "soft, mild," Greek meldein "to melt, make liquid," Latin mollis "soft, mild"), from root *mel- (1) "soft." Figurative use by c. 1200. Related: Melted; melting.

Of food, to melt in (one's) mouth is from 1690s. Melting pot is from 1540s; figurative use from 1855; popularized with reference to America by play "The Melting Pot" by Israel Zangwill (1908).