An approach to structural-parametric identification of boundary conditions of technological thermal physics processes based on the solution of inverse heat conduction problems is proposed. The stage of structural identification under conditions of a priori uncertainty is reduced to generation of alternatives of possible classes of solutions, which are given in the form of compact sets. Taking into account the restrictions on the membership of the solution to the corresponding classes, the initial incorrectly posed problem was decomposed into a set of conditionally correct problems. Parametrization of the identified characteristic and the resulting state function corresponding to it is carried out at the stage of parametric identification on the basis of the given model structure. Thus, the obtained problems are reduced to parametric optimization problems. Its solution is realized on the basis of methods of optimal control of systems with distributed parameters estimating of temperature discrepancy in a uniform metric. The analytical method of minimax optimisation, considering alternance properties of optimal distributions, allows solving mathematical programming problems concerning the values of the parameter vector for each of the formulated alternatives. The minimax criterion is used to select an appropriate mathematical model from all available variants. If necessary, the structure of the model can be refined by extending the classes of solutions. The presented approach demonstrates satisfactory quality of identification at typical modes of operation of thermal plants on sets of sufficiently smooth functions with the minimum possible number of parameters for the required accuracy of the solution. The aim of the approach is to provide information support for the decision making process on the structure of the model operator in inverse heat conduction problems. By generating hypotheses in the form of correctness classes parameterised by a vector of parameters of higher dimensionality, the quality of identification is improved in complex equipment operating modes.