A process for removing CO 2 from a flue gas stream containing CO 2, which process comprises: a) conducting said flue gas stream to a temperature swing adsorption gas separation unit wherein the gas separation unit contains at least one adsorbent contactor, wherein the adsorbent contactor is a parallel channel contactor having a plurality of open flow channels through which the flue gas stream flows, wherein the surface of said flow channels is comprised of an adsorbent material that is capable of adsorbing CO 2 from said flue gas stream, thereby resulting in a substantially CO 2 free flue gas stream and CO 2 adsorbed onto said adsorbent material, wherein the adsorbent material is comprised of a microporous material; b) venting said substantially CO 2 free flue gas stream into the atmosphere; c) heating said contactor having CO 2 adsorbed thereon to an effective temperature that results in the desorption of at least a fraction of CO 2 thereby resulting in a CO 2 -rich stream; d) compressing said CO 2 -rich stream to a pressure in excess of 6.9 MPa (1000 psig) thereby resulting in a compressed CO 2 -rich stream whose temperature has been substantially raised during compressing; e) cooling said compressed CO 2 -rich stream by use of a suitable heat-exchange fluid at a first temperature that captures heat from said CO 2 -rich stream thereby resulting in a CO 2 -rich stream of substantially reduced temperature and a heat-exchange fluid having a substantially higher second temperature; and f) using at least a portion of the heat from the heat-exchange fluid of substantially higher second temperature to provide heat to the contactor during the desorption step c) above. a) conducting said flue gas stream to a temperature swing adsorption gas separation unit wherein the gas separation unit contains at least one adsorbent contactor, wherein the adsorbent contactor is a parallel channel contactor having a plurality of open flow channels through which the flue gas stream flows, wherein the surface of said flow channels is comprised of an adsorbent material that is capable of adsorbing CO 2 from said flue gas stream, thereby resulting in a substantially CO 2 free flue gas stream and CO 2 adsorbed onto said adsorbent material, wherein the adsorbent material is comprised of a microporous material; b) venting said substantially CO 2 free flue gas stream into the atmosphere; c) heating said contactor having CO 2 adsorbed thereon to an effective temperature that results in the desorption of at least a fraction of CO 2 thereby resulting in a CO 2 -rich stream; d) compressing said CO 2 -rich stream to a pressure in excess of 6.9 MPa (1000 psig) thereby resulting in a compressed CO 2 -rich stream whose temperature has been substantially raised during compressing; e) cooling said compressed CO 2 -rich stream by use of a suitable heat-exchange fluid at a first temperature that captures heat from said CO 2 -rich stream thereby resulting in a CO 2 -rich stream of substantially reduced temperature and a heat-exchange fluid having a substantially higher second temperature; and f) using at least a portion of the heat from the heat-exchange fluid of substantially higher second temperature to provide heat to the contactor during the desorption step c) above.