For the classical representation of a numerical model of transient thermal conductivity the algorithmic stability has already been proved for most applications, but in this study we consider the problem of parametric adaptation of the transient thermal conductivity equation to the heated substance, which is represented as a solution of related variational problem. Particularly, we propose an approach, which is based on the substitution of the thermophysical parameters of the model under consideration by adjustable parameters and their tuning by the stochastic gradient method. In order to avoid being stuck inside the regions of instability in the course of such ’training’, constraints for the mentioned adjustable parameters need to be introduced. In this paper such constraints are obtained on the basis of proved stability conditions of the classical fininte-difference model of transient thermal conductivity. Numerical experiments have shown that the proposed constraints allow, on average, to increase the number of stable initial conditions by 14% and the number of stable training trajectories by 61%.