The industrial implementation of transient heat conduction models implies such a complicated process as their 'adaptation', which is known to be of two different kinds: to heated material and heating medium. In this study we use an alternative approach to heated material adaptation that is based on solution of variational problem. Its essence is to turn thermophysical parameters of transient heat equation, which are unknown and to be found, into non-dimensional values that cover all time grid. These values are: 1) used in the course of the forward solution of a transient heat conduction problem to compute the temperature of steel, 2) adjusted as far as the inverse solution is considered. The aim of this research is to modify the above-described method with the Huber loss function and compare the rate of convergence with the previously used quadratic loss function using different optimizers, such as the proposed one, ADAGRAD and ADADELTA. As a result, it is obtained that the Huber loss function does not increase the convergence rate for the problem under consideration. Additional experiments show that, unlike the proposed optimizer, the ADAGRAD and ADADELTA face the rapid gradient decay, which negatively affects the results of their application.