In recent years, the saturated adsorption capacity of novel adsorbents has been continuously enhanced. However, due to limitations in process design, the actual adsorption capacity of adsorbents during cyclic operation remains significantly lower than their saturated value. To establish an accurate adsorption bed model and investigate the complex heat and mass transfer mechanisms involved in the adsorption process, 13X molecular sieves were employed to conduct adsorption experiments on CO2/N2 gas mixtures. Through static adsorption experiments and dynamic breakthrough experiments, the competitive adsorption isotherms as well as the mass and heat transfer coefficients of the adsorption process were determined. Based on these fundamental data, a temperature swing adsorption (TSA) system model was successfully constructed, which accurately reproduced the breakthrough curves and temperature distributions under three distinct operating conditions. This adsorption bed model exhibited excellent performance in reflecting real-world adsorption behavior, particularly in scenarios involving low gas concentrations. The analysis of the loading condition of the adsorption bed indicated that the adsorbent utilization ratio (AUR) of the conventional TSA process was only 58.13%, with a significant amount of adsorbent not being fully utilized. Therefore, a novel multi-bed series TSA adsorption process was designed in this study. By switching different adsorption beds between the upstream bed and the downstream bed, the AUR was increased to 85.50%. Concurrently, the product purity increased from 90.74% (conventional TSA process) to 94.21%, and the energy consumption decreased from 6.48 MJ/kg CO2 to 4.79 MJ/kg CO2. However, the series process had a small amount of CO2 leakage during the adsorption stage, resulting in a gas recovery rate of 87.92%. In addition, although the conventional TSA process can achieve the similar AUR as the series process by extending the adsorption time, its recovery was only 71.80%, which was 16.12 percentage points lower than that of the novel series process.