A portable computer docking base has incorporated therein a plug-in cooling system used to provide auxiliary operating heat dissipation for a portable notebook computer moved through a docking path along the base into a docked relationship therewith. The docking base cooling system has a fan-cooled heat sink member disposed within its housing, with a thermal plug structure projecting outwardly from the heat sink into the docking path. As the computer reaches its docked orientation on the base, the thermal plug is received in a socket within a heat sink portion of the computer's internal cooling system. The mated plug and socket portions of the two cooling systems form a thermal link therebetween that permits computer operating heat to be transferred to the docking base heat sink for dissipation therefrom. In one embodiment thereof the thermal plug structure is partially defined by an outwardly projecting evaporating end portion of a thermosyphoning heat pipe. In another embodiment thereof, the outwardly projecting thermal plug structure is integrally formed with the internal docking base heat sink and comprises opposing metal plug sections separated by a resilient material. When the plug structure enters the computer heat sink socket, the plug sections are resiliently forced toward one another to provide a socket clamping force on the received plug structure and increase the socket-to-plug heat transfer efficiency.