<p>This study investigates the structure of shock waves in carbon dioxide gas utilizing the one-temperature and the multi-temperature models within the Navier–Stokes–Fourier framework. The gas behavior is described using the reduced van der Waals equation of state, with temperature-dependent internal energy partitioned into translational, rotational, and vibrational components, each defined by distinct temperatures in the multi-temperature model. An implicit system of equations for temperature-dependent viscosity and thermal conductivity is derived and solved numerically to analyze velocity and temperature profiles. We observed that the overall temperature decreases with an increase in the number of active vibrational modes of carbon dioxide. Moreover, we found that an increase in the Mach number leads to the loss of symmetry in the overall temperature profile within the multi-temperature approach. Significant variations are observed in temperature, density, the inverse of shock thickness, molar specific heat at constant pressure, and the ratio of bulk-to-shear viscosity, influenced by the number of active vibrational modes, pre-shock Mach number, and the non-ideal behavior of the gas. Additionally, we demonstrate that the slow relaxation of temperature in the multi-temperature model is more effectively represented by temperature shock thickness rather than the conventional velocity shock thickness. Our findings indicate that both one-temperature and multi-temperature models, along with various modes of molecular motion coupled and uncoupled play critical roles in shaping the structure of shock waves.</p>