Supplementary cooling elements in addition to a primary cooling element of a furnace. The supplementary cooling elements, with two or more components, may be inserted from the outside of the furnace into holes that pass through and the primary cooling element such that the cooling elements protrude beyond the inner surface of the primary cooling element. An inner one of the components of the supplementary cooling element may be received by an outer one of the components in a manner that forces the outer component into a thermally conductive pressure connection with the primary cooling element.