The equations of hydrodynamics including conduction of heat are solved numerically by using the finite element method. The heat flow is calculated according to the Fourier's heat conduction. The temperature on the contact side of elements is calculated by the continuity condition of heat flow. According to triangular partitions divided from a quadrangle side of body element, convection heat flow is calculated. Considering the isotropic-elastic-plastic-hydrodynamic material model, the equation of state with three contributions, and the correlation between thermal conductivity and temperature, some computational examples, including the Fourier's heat conduction, contact heat transfer, deformation effects of heat, and shock compression of mixture, are given by the finite element code. The numerical simulation of shock temperature of mixture indicates that the temperatures among minute grains fluctuate, and tend to reach a thermal equilibrium during the shock propagation.