Display omitted •Rapid thermal swing adsorption process with multi-fixed beds was proposed for CO2 capture.•Internal heat integration was made by recovering sensible heat from the cooling process.•CO2 cyclic capacity of hollow fiber sorbents was improved via multiple adsorption processes.•The energy performance of proposed RTSA process was evaluated by experiments and modeling. A rapid thermal swing adsorption (RTSA) process with heat integration is considered to be an energy-efficient method for large-scale CO2 capture. Herein, we propose a new heat-integrated RTSA process for post-combustion CO2 capture as a proof-of-concept based on rationally designed multi-fixed beds by incorporating the internal heat integration concept of the moving bed adsorption process. Our proposed RTSA process consists of multiple beds, each of which undergoes four sequential processes, including adsorption, heating, desorption, and cooling in a continuous cyclic mode. Also, the switching time of adsorption/desorption process is determined by CO2 adsorption/desorption kinetics while that of the heating/cooling process is determined by the heat transfer rate. Our unique RTSA design enables internal heat integration by recovering sensible heat from the cooling process. Furthermore, it can enhance the CO2 cyclic capacity of hollow fiber sorbents with high CO2 recovery by performing multiple adsorption processes simultaneously. Most importantly, our economic analysis based on experiments and rigorous mathematical modeling revealed that the energy demand of the optimized RTSA process is estimated to be approximately 272 kWh/t-CO2 with 58% sensible heat recovery. Such low energy penalty is comparable to that of the most mature amine-based absorption process (271 kWh/t-CO2) due to a combination of internal heat integration and enhanced CO2 cyclic capacity, supporting the feasibility of a RTSA process for post-combustion CO2 capture.