A portable computer docking base has incorporated therein a thermoelectric cooling system used to provide auxiliary operating heat dissipation for a portable notebook computer operatively docked to the base. The cooling system includes a thermoelectric (Peltier effect) heat pump unit disposed within the docking base housing and having opposite hot and cold sides. A finned heat sink member is secured to the hot side of the assembly and positioned in the path of fan-generated cooling air, and a heat slug member is secured to the cold side of the assembly and projects outwardly through an exterior wall of the docking base housing into its computer receiving area. When the computer is placed in the receiving area and docked, the cooling system heat slug member is brought into heat conductive contact with a similar heat slug member carried within the computer and thermally coupled to its microprocessor. Operating heat from the microprocessor is transferred through the contacting heat slugs, passes through the thermoelectric heat pump assembly to its hot side heat sink, and is dissipated from the heat sink to the cooling air flow within the docking base.