A heat exchanger for cooling an array of electric circuit chips disposed on a common substrate is formed as a flexible sheet of thermally conducting material with upstanding fins for transference of heat from the chips to a coolant flowing through the fins. The sheet may be provided with corrugations set between sites of the chips for improved flexibility to accommodate individual orientations of the chips. The sheet is sufficiently large to cover an array of chips and is secured adheringly, as by use of a thermally conductive grease, to the chips. The sheet hermetically seals the chips from contamination by the coolant. The heat exchanger may be fabricated of copper with a nickel coating, wherein the copper provides the heat conduction and the nickel protects the copper from a corrosive coolant such as water. The finned sheet may be efficiently fabricated by processes analogous to those used to make printed circuits. In one embodiment of the heat exchanger, the fin thickness, the fin spacing and the sheet thickness are all approximately equal, a typical sheet thickness being approximately two mils.