  Considering high-temperature heating, the equations of transient heat
conduction model require an adaptation, i.e. the dependence of thermophysical
parameters of the model on the temperature is to be identified for each
specific material to be heated. This problem is most often solved by
approximation of the tabular data on the measurements of the required
parameters, which can be found in the literature, by means of regression
equations. But, for example, considering the steel heating process, this
approach is difficult to be implemented due to the lack of tabular discrete
measurements for many grades of steel, such as alloyed ones. In this paper, the
new approach is proposed, which is based on a solution of a related variational
problem. Its main idea is to substitute the adaptation process in the classical
sense (i.e., to find the dependencies of thermophysical parameters on
temperature) with 'supervised learning' of a mesh model on the basis of the
technological data received from the plant. The equations to adjust the
parameters of the transient heat conduction model, which are related to the
thermophysical coefficients, have been derived. A numerical experiment is
conducted for steel of a particular group of grades, for which enough both
technological as well as tabular data are available. As a result, the 'trained'
mesh model, which has not received explicitly any information about the
physical and chemical properties of the heated substance, demonstrated an
average error of 18.820 C, which is quite close to the average error of the
model adapted classically on the basis of the tabular data (18.10 C).
