gʷher-mn̥-
“warm thing, heated substance”furnace, furnish, thermal
Nominal of *gʷher- giving Latin fornus > furnace, furnish; Greek thermos > thermal.
Discussion
The PIE form *gʷher-mn̥- (warm thing, heated substance) derives from the root *gʷher- (warm, hot), with the *-mn̥- suffix producing a result noun: "the thing that is warm" or "that which warms." The root produced vocabulary for heat, warmth, and the technology of heating across the major branches.
Latin formus (warm) and the derivative fornāx (oven, furnace — the warming device) continue the root with the expected Italic treatment of the labiovelar: PIE *gʷh > Latin f. From fornāx English inherits furnace (the heating chamber), furnish (from Old French fornir, "to provide/equip" — originally to equip with warmth/provisions), and the rare fornicāte — Latin fornix ("arch, vault" — the vaulted ceiling of an oven) came to mean "brothel" because Roman prostitutes worked under the arches of public buildings, giving English fornicate from a PIE word for warmth.
Greek thermós (θερμός, "warm, hot") preserves the root with the expected Greek treatment and is far more productive in modern English: thermal (pertaining to heat), thermometer (heat-measurer), thermos (the insulated flask — originally a brand name), thermostat (heat-stander — a device that keeps temperature standing/constant), thermodynamics, and hypothermia (under-heat — dangerously low body temperature).
Sanskrit gharmá- (heat, warmth) continues the Indo-Iranian reflex. The Vedic gharma is both physical heat and the ritual heat of sacrifice.
Old English wearm (warm) continues the root through the Germanic branch: PIE *gʷh > PGmc *w (the labial component of the labiovelar survives while the velar is lost). English warm and German warm are thus cognates of Greek thermós — a correspondence that surprises most speakers but follows regular sound laws.