A method of attachment of a thermally conductive element (28) to an electric circuit chip (22) for cooling the chip includes initial steps of forming an oxide-free preform (56) of a fusible metal alloy (50) by extrusion of alloy between two mold blocks or plates (38, 40). During the extrusion, the oxide coating (54) is left behind so that the extruded alloy is essentially free of oxide. The extrusion takes place at a temperature elevated to approximately the liquidus temperature of the alloy. The preform, which may be in the form of a pill (56) or section (74) of thin foil, is placed between interfacing surfaces of the thermally conductive element and the chip, and is then extruded along the interfacing surfaces under pressure and elevated temperature to form a thermally conductive, oxide-free bonding layer of superior thermal conductivity.