A novel multibed heat-integrated vacuum and temperature swing adsorption process has been designed to capture 85% of the CO2 emitted by an advanced supercritical coal fired power plant of 820 MWe taken as reference, and to produce a concentrated product with 95% of CO2 using a microporous carbon obtained from olive stones. The overall performance of the post-combustion CO2 capture process has been evaluated from the results of the dynamic simulation of the process at cyclic steady state, using a detailed non-isothermal non equilibrium dynamic fixed-bed adsorption model that takes into consideration competitive adsorption between the main flue gas components: N-2, CO2 and H2O. The proposed process operates between 30 degrees C and 1.05 bar and 80 degrees C and 0.05 bar. The specific heat duty of the process, 2.41 MJ(th) kg(-1) CO2, which is lower than the benchmark amine absorption technology, can be satisfied using waste heat. On the other hand, its electricity consumption, 1.15 MJ(e) kg(-1) CO2, is higher. Increasing the pressure of the production step reduces significantly the energy demand of the process, but also its capture rate. Substantial improvements in performance can be expected from adsorbent development. Adsorption is an environmentally benign technology with great potential to mitigate CO2 emissions from industrial processes with unused waste heat sources.