The Statistical Inelastic Cross-Section (SICS(D)) model for molecules with discrete rotational energy is used for the Monte Carlo simulation of rarefied nitrogen gases contained between two parallel plates at a large temperature difference with the null-collision direct-simulation Monte Carlo method to compare with the density distributions measured by Alofs et al. Good agreement is found between the experimental and Monte Carlo results for the fully diffuse reflection plates. The rotational distribution near the cold plate indicates the bimodal form represented approximately by the merging of two Boltzmann distributions at the cold and hot plate temperatures.