A non-equilibrium heating situation occurs when the intensity of heat flux,is high and the heating duration is shorter than the thermalization time of the substrate material. In the present study, the heating of gold due to time exponentially decaying surface heat flux is considered. Electron and lattice site temperatures are predicted from the electron kinetic, theory approach. To quantify the thermodynamic irreversibility in the thermal system, entropy analysis,in the electron and lattice subsystems is performed and thermal communication between both systems is formulated. It is found that electron and lattice subsystems separate thermally. Electron temperature rise is rapid while lattice temperature rise is gradual during the early heating period. Volumetric entropy generation in the electron subsystem is higher than it is in the lattice subsystem.