A low-cost, high-temperature heat exchanger is made from a notched piece of metal, the metal being folded back and forth upon itself to form a monolith. The notches in the metal piece create openings, communicating with distinct sides of the monolith. Ducts are attached to the openings. Cut pieces of corrugated metal, which may have a catalyst coating, are inserted between folds of the monolith. The heat exchanger may be used as part of a fuel cell system, or in other industrial applications, to recover waste heat, or to conduct various catalytic and non-catalytic reactions. The invention also includes an element, or building block, for a high-temperature heat exchanger, including a folded metal monolith with metal combs inserted, the monolith and the combs defining seams which are hermetically sealed.