From Latin 'fornāx' (oven), from PIE *gʷʰer- (warm, hot) — the same root behind 'warm' and 'thermal.'
An enclosed structure in which material can be heated to very high temperatures; a device for heating a building.
From Old French 'fornais' (furnace, oven), from Latin 'fornāx' (an oven, a kiln, a furnace), from 'fornus' (an oven), related to 'formus' (warm). The PIE root is *gʷʰer- (warm, hot), which also gives English 'warm' (through Germanic) and 'thermal' (through Greek 'thermos'). A furnace is thus etymologically a 'warm-making' device. Key
English 'furnace,' 'warm,' and 'thermal' all trace to the same PIE root *gʷʰer- (warm, hot). The Latin branch gave 'furnace' and 'fornicate' (yes, really — 'fornix' meant a vaulted arch or cellar, and Roman prostitutes worked in vaulted basement rooms, so 'fornicārī' meant to frequent such places). The Greek branch