kerH-mn̥-
“heating device, oven, furnace”kiln, ceramic, cremation
Nominal of *kerH- giving English kiln, Greek keramos > ceramic, Latin cremāre > cremation.
Discussion
The PIE form *kerH-mn̥- (heating device, furnace) derives from the verbal root *kerH- (to burn, to heat), with the instrumental suffix *-mn̥- producing a noun of means: "the thing that burns/heats." The root generated vocabulary for heat, ceramics, and cremation across the major branches.
Latin cremāre (to burn, to reduce to ashes) continues the root with the specific sense of combustion, and its derivatives entered English through the vocabulary of death and materials: cremate, cremation, crematorium. The practice of cremation was widespread in PIE-descendant cultures, and the word's survival suggests the practice may have PIE roots — a point debated in archaeological literature.
Greek kéramos (κέραμος, "potter's clay, pottery, tile") preserves the root with a crucial semantic shift: from burning to the product of burning. Fired clay — ceramic — is material defined by its encounter with heat. From kéramos English derives ceramic and the Kerameikos, the potters' quarter of ancient Athens where the cemetery was located (the association of pottery and burial giving the neighbourhood a double significance). The ceramic connection implies that PIE speakers were familiar with fired pottery, a detail consistent with the archaeological record for the proposed homeland period.
Latin carbō (charcoal, ember — the product of incomplete burning) may be from a related root, giving English carbon, carbonize, and charcoal itself (from char + coal, where char may derive from a related PIE form). The entire vocabulary of carbon chemistry — carbonate, carbohydrate, hydrocarbon — rests on a PIE root for burning.
Old English heorþ (hearth) is sometimes connected to this root through a different formation, though the phonological derivation is debated. If correct, the hearth — the central fire-place of the Germanic home — shares its name with the PIE word for burning, and the English phrase hearth and home encodes a five-thousand-year-old association of fire with domestic security.
The suffix *-mn̥- in *kerH-mn̥- is the same instrumental formation found in *srew-mn̥- (stream, the thing that flows) and *bʰewd-mn̥- (bottom, the thing pushed down). The pattern ROOT + *-mn̥- consistently produces nouns for the product or instrument of the verbal action.