To overcome the high carbon dioxide-specific energy input in temperature swing adsorption concepts for direct air capture processes, an application of highly heat-integrated process concepts is being investigated. The detailed modeling and simulation of a belt and a moving bed adsorber concept indicates that a recovery of the sensitive heat of the adsorbent of more than 90 % can be achieved. Here, a combination of the presented concepts with a power-to-gas process opens up the potential for the realization of an autothermal overall process design.