Since in a number of cases it is technically difficult and sometimes impossible to directly measure some parameter at the specified point of the object measurement based on theoretical and experimental simulation of the physical fields with introduction of computer technology made it possible to indirectly determine various values at difficultly accessible or inaccessible points of the object. The method makes it possible to use thermal transducers the upper limit of which is below the measured temperature. Such extrapolation problems are pressing ones in metallurgy, gas dynamics, and o~her areas of technology in which such an approach is frequently the only method of obtaining adequate results.In solution of reverse problems of the theory of a field the nonreal course of a physical process converted from the consequence Bo the reason is considered. In view of the noncorrespondence to physically realizable eventsthese problems belong to the class of incorrectly formulated [i]. This means that in solution of them conditions of regularity (uniqueness) are not fulfilled. Small errors in the original data may lead to large errors in the identifiable parameters, which is especially characteristic in solution of kind I Volterra type integral equations [2, pp. 27-30].An excess of experimental information on the temperature-dependent parameters of an object (inertial lag of the reaction to a sharp disturbance, electrical resistance of the active layer, etc.) provides regularity of solution of reverse problems and makes it possible to reduce them to realization of algebraic analogs.Let us consider the problem of synthesis of the reason based on the consequence described by the reverse problem of transfer with sinks of heat and mass, that is, the reverse problem of thermal conductivity with mobile boundaries occurring in such an object as the lining of a steel melting converter. In the laboratory it is practically impossible to create the real service conditions of the lining in a converter. Therefore all of the investigations were made on a production converter.During blowing of the converter bath heat exchange occurs between it and the lining with a type III boundary condition on the heated surface of the brick according to the equation ot (1) =(t.--t[~=o)= --k~x "Promavtomatika" KNPO.