The relaxation equation of heat conduction and generation is solved by method of Laplace transforms for the case of a Semi-infinite body and an arbitrary dependence of the surface temperature on time. For the case of equality of the relaxation time of the heat flux (tau(k)) and the relaxation time of the internal heat source capacity (tau(g)) the Laplace domain solution is inverted analytically, otherwise numerically. Exemplary calculations are carried out for the surface temperature function in the form of a rectangular pulse. The results show that significant differences can occur between the relaxation and parabolic models, in qualitative as well as quantitative terms, which do not disappear for large times. A long-time relaxation solution for tau(g) = 0 tends to overlap with the corresponding parabolic solution of a case with heat generation, whilst a long-time relaxation solution for tau g = infinity tends to overlap with the corresponding parabolic solution of a case without heat generation.