Carbon dioxide (CO2) capture and storage (CCS) and most CO2 capture and utilization (CCU) routes require concentrated CO2 streams for efficient compression, pipeline transport, injection, or chemical syntheses. The achieved quality of the CO2-rich product stream greatly influences the energy effort for CO2 capture, resulting in widely scattering figures for CO2 capture effort in the literature. The present article specifically addresses the provision of concentrated CO2 (>99 vol %) from diluted sources. A continuously operated temperature swing adsorption process (TSA) is chosen to illustrate the technical challenges. A detailed steady-state process model is used for the thermodynamic evaluation that had previously been developed for the commercially available solid sorbent Lewatit VP OC 1065. Three typical inlet concentrations of CO2 corresponding to atmospheric air (0.04 vol %(db)), gas turbine combined cycle exhaust gas (4 vol %(db)), and solid fuel combustion exhaust gas (10 vol %(db)) are investigated. Each case has been optimized in terms of stage configuration, sorbent circulation rate and stripping steam rate. For capture from air with a capture rate of 50%, two stages are used in the adsorber and 10 stages are used in the desorber, while for the capture from both exhaust gas mixtures, a capture rate of 90% and a 4 x 4 stage configuration are used. The specific total energy demand for capture and concentration turns out to be 10 times higher for capture from ambient air (25.76 MJ/kg(CO2) heat @ 120 degrees C + 8.26 MJ/kg(CO2) power) compared to capture from combustion exhaust gas with 4 vol %(db) (3.64 MJ/kg(CO2) heat @ 120 degrees C + 0.09 MJ/kg(CO2) power) and 10 vol %(db) (3.21 MJ/kg(CO2) heat @ 120 degrees C + 0.04 MJ/kg(CO2) power). A simple exergy analysis shows about three times higher irreversibilities in the case of capture from atmospheric air compared to capture from the two more concentrated source streams.