The disclosure relates to a continuous or semi-continuous, cyclic, countercurrent sorption-desorption method for enhanced control, separation, and/or purification of CO2 gas from one or more sources of a mixture of gases through integrated use of solid monolithic sorbents having a sorption selectivity for the CO2 gas, wherein liquid phase water is added to increase the heat capacity of the mixed gas source(s) in order to achieve a thermal wave moving through the thickness of the sorbent material faster than the CO2 sorption wave.