A multi-step process for removing CO2 from a process gas stream having CO2 and other gaseous components commences by adjusting the temperature of a CO2 laden process gas stream to be between about 80° and about 500° C. A first part of the temperature adjusted process gas stream is taken and contacted with a adsorbent in thermal contact with a heat-exchange surface. The remainder of said temperature adjusted process gas stream is taken and contacted with said heat-exchange surface to transfer heat to said adsorbent, thus causing any adsorbed CO2 to be desorbed for collection, and to cool said process gas stream remainder and removing any condensate from said cooled process gas stream remainder. The cooled process gas stream remainder is passed in contact with a cooled section of said adsorbent to adsorb CO2 therefrom, producing a CO2 depleted process gas stream. The desorbed CO2 is withdrawn for collection. The CO2 depleted process gas stream is passed into contact with heated regenerated adsorbent to cool it sufficiently for return of the process. Finally, any fines are withdrawn for collection.