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This paper considers the thermal problems associated with the design of high component-density encapsulated circuits, constructed with small solid-state components. The thermal resistance to the dissipation of component-generated heat is shown to consist of that of the encapsulating medium, plus that of the external circuit cooling process. Because the external cooling becomes more difficult as the size of an encapsulated circuit is reduced, a method of constructing such circuits is proposed which minimizes the thermal resistance due to the encapsulating medium. This construction makes a large fraction of the allowable component temperature rise available for use in the external heat dissipation process by providing high thermal conductance paths for the transfer of heat from the surfaces of the components to one surface of the circuit structure. Analytical models are developed for the most important heat transfer processes in the proposed circuit structure. The equations based on these models are arranged in a form suitable for design use, and example designs are presented.