Summary: Earlier we proposed numerical solutions of initial-boundary value problems for the semi-empirical model of heat conduction and modified this model by introducing more realistic approximations of the constitutive functions, basing on measured specific heat, heat conductivities and second sound speeds for NaF at low temperatures \((10\dots 20^\circ K)\). In the present paper, we suggest a method to choose the free parameters entering the constitutive functions by minimizing an error functional, measuring the differences between the theoretical and experimental heat pulses.