A temperature-vacuum swing (TVS) process, capable of extracting pure CO2 from dry and humid atmospheric air, is experimentally analyzed. Adsorption/desorption cycles utilizing a packed bed of a sorbent material made of diamine-functionalized commercial silica gel are performed under equilibrium and non-equilibrium (short-cycle) conditions. Thereby, the CO2 capture capacity of the material is determined over a wide range of operational parameters, namely 10–150 mbarabs desorption pressure, 74–90 °C desorption temperature, and 0–80% relative humidity during adsorption. Up to 158 ml of CO2 (6.8 ml per gram sorbent) with a purity of up to 97.6% is recovered per cycle. Adsorption isotherms of the sorbent material are experimentally determined by thermogravimetry and fitted to isotherm models, which are successfully applied to predict desorption capacities achieved in the TVS process. Under dry conditions, desorption pressures above 100 mbarabs lead to strongly decreasing CO2 capture capacities below 0.03 mmol g−1. Under humid conditions with 40% relative humidity during adsorption, the desorption pressure can be raised to 150 mbarabs with capture capacities remaining above 0.2 mmol g−1. Stable performance of the sorbent material in the TVS process is demonstrated over 40 consecutive adsorption/desorption cycles.