The choice of effective operating conditions for heat exchange equipment is an urgent task for the chemical, energy and related industries. To solve the inverse problem of heat transfer, first, the coordinate of the point of the beginning of the phase transition is found, then the heat exchange area and the degree of extraction of moisture and thermal energy from the exhaust gases are determined. The obtained solution of the inverse problem makes it possible to justify the choice of the design of the apparatus and its mode of operation while providing a given fraction of the release of moisture and thermal energy from flue gases under various conditions of the process organization. The found amount of utilized thermal energy and moisture from flue gases is an important technical and economic indicator of equipment functioning. In the future, the proposed approach can serve as the basis for solving inverse problems for complex heat and mass transfer systems with an arbitrary configuration of coolant flows in the implementation of a phase transition both in one and in several coolants.