Shock wave experiments show that many annealed face-centered cubic metals exhibit an anomalously increasing yield strength with temperature at high strain rates. Such an increase is usually associated with the multiplication of dislocations in the phonon friction mode, which slows with temperature. However, the effect of temperature on the structure of the shock wave and the yield strength of metal crystals, including those with microstructure, remains elusive. In this paper, we perform molecular dynamic simulations of shock-wave loading for [110] and [111] copper crystals of 0.45 and 0.80 micrometer length in a wide range of temperatures between 100 and 1100 K to understand the role of temperature and preexisting dislocations on the Hugoniot Elastic Limit (HEL). We show that, in ideal copper crystals, the elastic precursor exhibits a form of plateau, and the HEL almost does not change with shock propagation distance. However, at higher impacts, the perturbations of an elastic precursor are observed which leads to fluctuation in the HEL value. We show that temperature dependencies of the HEL are strongly anisotropic. The HEL values tend to decrease with temperature for [110] perfect copper crystals, and to increase with temperature for [111] copper crystals. This surprising result is explained by the presence of dislocation substructures in a plastic wave in [110] crystals, which reduces the mobility of dislocations and makes the process of dislocation nucleation more dominant than in [111] crystals. Preexisting dislocations in copper crystals allow the HEL to decay much faster than in ideal crystals. In contrast to ideal [110] crystals, [110] crystals with dislocations exhibit increasing HEL values with temperature, as do [111] crystals. We find that the HEL dependence could be well approximated by a power law, but the decay power changes as the wave propagates. The decay power values lie between 0.5 and 0.7 in the second stage for both [110] and [111] crystals, which is consistent with experimental results with polycrystalline annealed copper. Our findings extend our understanding of temperature-dependent mechanical properties of materials under high strain rate and crystal plasticity.