While the density profile of a granular shock front can be obtained by the conventional treatment of supersonic fluids, its temperature profile is very different from that in ordinary shocks. We study the density and temperature profiles of a traveling granular shock generated by piling up metal spheres in a closed bottom quasi-two-dimensional channel. We successfully account for the temperature profile in the granular shock using a simple kinetic theory in terms of energy transfer from the mean flow direction to the transverse direction. Contrary to ordinary fluids and previous granular shock experiments, the granular shock width is found to increase with the inflow rate.