This paper presents the thermo-mechanical coupled model of single crystal based on rate-dependent plastic slip deformation theory and its FEM algorithm. The model includes two aspects: one is irreversible heat resulted by plastic deformation and another is a large amount of thermal stress from temperature changing under rapid thermal shock effect. Formulas of shear strain rate and shear modulus dependent on temperature are also given, and the subroutines to calculate stress and strain are coded based on ABAUS software. The relations among stress, strain and temperature of <001>/{100} single crystal copper under tension conditions are calculated by the model established. The results show that true stress are proportional to temperature at first and then nonlinear decreasing but true strain are increased with temperature increasing, so elastic modulus decreases with increasing plastic deformation. The numerical results are consistent with those simulated by molecular dynamics. It shows that the model and its FEM algorithm are reasonable, and their computing costs are less and less than MD simulation.