According to the ideal fluid dynamics approach, the temperature and entropy values of a medium undergo a jump increase in the shock front as well as on contact interface between different materials after the shock wave propagation, but remain constant behind the shock front out of the contact interface. In the real condensed matter, the shock fronts and transition regions near the interfaces have finite thicknesses; therefore, the temperature field is disturbed around the interfaces. In this work, such disturbances are numerically analyzed for the problems of formation of the steady shock wave at impact and ramp loading of metals, reflection of the steady shock wave from a free surface, and the shock wave passing through the interface between two different materials. Theoretical analysis and computations show that the non-isentropic layers (the high-entropy ones with the increased temperature and the low-entropy ones with the decreased temperature) arise near the interfaces in the above problems of shock and ramp loading. The impact produces the high-entropy layer; while the ramp loading can result in the both high-and low-entropy layers. At the shock wave passing through the interface, the high-entropy layer is formed in the lower-impedance material and the low-entropy-in the higher-impedance one. These high-and low-entropy layers should be taken into account in simulations of shock-wave processes in thin targets or in other cases where surface effects are important. For example, melting can take place in the high-entropy layer on the interface between colliding plates at shock intensities lower than the bulk melting threshold; also the temperature perturbations near the studied surface can affect the result of pyrometric measurements. To get high accuracy of simulations, one should exclude the artificial viscosity or its analogs from the numerical scheme and use the physically based dissipative processes (the physical viscosity, the plasticity, and the heat conductivity) for stabilization of the solution instead. Such a mathematical model with accounting for the dislocation plasticity is described here as well as the appropriate numerical scheme is proposed.