This paper proposes a novel design of a thermal swing adsorption (TSA) system with a cooling jacket and compares it with conventional TSA processes by cyclic simulations. The purposes are to increase the adsorption efficiency and to find a suitable condition for its application to a two-bed TSA system for continuous operation. These processes purify the ternary mixtures consisting of benzene, toluene, and p-xylene. The models are based on nonequilibrium, nonisothermal, and nonadiabatic conditions. The breakthrough curves of our simulation model are compared with that of Yun's experiments (Ph.D. Thesis, Korea University, 1999). As a result of the continuous simulation from startup to the cyclic steady state (CSS), the augmented ratio of the amount adsorbed of jacketed TSA system to the conventional one at CSS is 20.3% for a two-step operation and 6.3% for a three-step operation, respectively.