A converging design multi-chip module having semiconductor chips connected to a substrate recessed into a cavity of the MCM package body, the chips being interconnected using flip chip and control collapse chip connection, wherein a metal heatspreader plate is adapted to engage the backside of the chips and is held in place by an attachment ring welded to the package body. Alternatively, the heatspreader plate can be glued directly to the backside of the chips using a high thermal conductivity and low modulus cement. One or more electrically passive thermal shunt chips are disposed between the substrate and the heatspreader plate for additional heat conduction. In a preferred embodiment, the attachment ring is made from KOVAR.RTM. and has a thermal coefficient of expansion that is about the same as that of the package body. Thermal grease is interposed between the heatspreader plate and the semiconductor chips for improved heat transfer. In an alternative embodiment, the heatspreader plate is directly shunted to the substrate. In another alternative embodiment, the heatspreader plate is urged against the chips by a spring plate or a coiled spring against a lid for the package cavity.