The continuous quest for improving the performance of heat exchangers, together with evermore stringent volume and weight constraints, especially in enclosed applications (engines, electronic devices), stimulates the search for compact, high-performance units. One of the shapes that emerged from a vast body of research is the disc-shaped heat exchanger, in which the fluid to be heated/cooled flows through radial -often bifurcated- channels inside of a metallic disc. The disc in turn exchanges heat with the heat/cold source (the environment or another body). Several studies have been devoted to the identification of an “optimal shape” of the channels: most of them are based on prime principles, though numerical simulations abound as well. The present paper demonstrates that -for all engineering purposes- there is only one correct design procedure for such a heat exchanger, and that this procedure depends solely on the technical specifications (exchanged thermal power, materials, surface quality): the design in fact reduces to a zero-degree of freedom problem! The argument is described in detail, and it is shown that a proper application of the constraints completely identifies the shape, size and similarity indices of both the disc and the internal channels. Goal of this study is not that of “inventing” a novel heat exchanger design procedure, but that of demonstrating that -in this as in many similar cases-a straight forward application of prime principles and of diligent engineering rules may generate “optimal” designs. Of course, the resulting configurations may be a posteriori tested as to their performance, their irreversibility rates, their compliance with one or the other “techno-economical optimization methods”, but it is important to realize that they enjoy a sort of “embedded” optimality.