A number of mathematical models, digital twins and diagnostic systems are considered, which are used for individual processes and elements of flame furnaces. An idea was put forward about the expediency of creating a complex digital twin, which simultaneously takes into account the main processes in metal heat processing (heating for rolling or heat treatment) in a flame furnace. A conceptual definition of the structure and interconnection of the elements of a complex digital twin of a furnace for metal heat processing is carried out. It is substantiated that the data to ensure the operation of the digital twin are divided into two groups: constantly or periodically measured values and data that are unchanged. The minimum set of quantities, the measurement of which is necessary for the operation of the proposed complex digital twin of the furnace, is determined. A list of objective data about the unit and the technological process, which are unchanged over a long period of operation, is also compiled. At the same time, a scheme for organization the interaction of special computing units has been developed, which allows to achieve high accuracy in solving the traditional problem of mathematical modeling of metal heat processing ‒ determining the metal temperature field. To achieve this result, computing units are used to identify the parameters of all processes that affect the solution of the problem: the value of air suction into the furnace chamber and along the smoke path, the value of the recovery coeffi-cient, the oxygen consumption for the oxidation of the metal surface, the average heat flux density absorbed by the metal surface. Special blocks are also provided for diagnosing the state of the heat exchanger, fan, smoke path, chimney and elements of the mechanical equipment of the furnace. Ultimately, top-level blocks are provided that allow, based on the processing of information from all the basic blocks of the complex digital twin, to analyze the energy efficiency of the furnace unit, obtain the technical and economic characteristics of its operation, as well as to issue recommendations to clarify the current parameters of technological processes and maintenance of equipment elements.