A method is disclosed for mounting and cooling a circuit component having a plurality of contacts. The method comprises mounting the circuit component on a rigid substrate of a thermally conductive material having and electrically insulating regions with a circuit board arranged between the circuit component and the substrate. The circuit board, which carries conductive traces that terminate in contact pads, is secured to the substrate with at least some of the contact pads on the circuit board disposed on the side of the board facing the substrate, some of which being bonded to the substrate. To establish both an electrical and a thermal connection between the contacts of the circuit component and the contact pads bonded to the substrate, blind holes are formed in the base of the circuit board, each hole terminating at a respective one of the contact pads bonded to the substrate.