<p>A region of physical realizability of two- and multiflow heat transfer has been constructed in the space of thermodynamic indicators: heat load, energy dissipation, and thermal conductivity coefficient. The boundary of this region is achievable in a counterflow displacement heat exchanger, provided the conditions placed on the flows’ heat capacities are observed. Using the concept of thermodynamic equivalence of a two-flow heat exchanger and a multiflow system, the requirements for an optimal heat exchange system have been formulated. It is shown that the dependencies of the cold and hot flows’ temperatures on the heat load in an equivalent heat exchanger constructed using the suggested algorithm determine the total number of two-flow cells in the system, their heat loads, the heat transfer coefficients, entropy production, and the structure of the contacts. In this case, each hot flow in an optimal system can be in contact with several cold ones, and each cold flow can contact several hot ones.</p><p>Cases of flow state phase variation have been considered. Limitations placed on the temperatures of all or part of the flows at the inlet and outlet of a heat exchange system have been taken into account. An algorithm has been suggested for selecting free parameters of flows, their heat capacities, boundary temperatures, and distribution of contact surfaces.</p>