Abstract: An apparatus for molding composite articles includes a pair of opposed matched-tool mold sections, each having a rigid housing and a thin, semi-rigid membrane removably and sealably mounted on the housing so as to define a fluid-tight chamber therein. The chamber of each mold section is filled with a noncompressible heat-conductive fluid to provide fluid backing to the portions of each membrane defining the molding surfaces of each mold section. A system of temperature control coils extending within each chamber are connected to an external heater/chiller unit to permit circulation therethrough of a suitable temperature control fluid, whereby positive control of the temperature of the backing fluid and, correlatively, the molding surfaces of the membranes.