A temperature swing adsorption process for removing a target component from a gaseous mixture containing at least one side component besides the target component, said process being carried out in a plurality of reactors (101, 102, 103), wherein each reactor performs the following steps: (a) an adsorption step, comprising contacting an input stream of said gaseous mixture with a solid adsorbent and adsorption of target component from said input stream, providing a target component-loaded adsorbent and a first waste stream depleted of the target component; (b) heating of said loaded adsorbent and desorption of a first amount of target component, providing a partially regenerated adsorbent and a first output stream containing the desorbed target component; (c) cooling of said at least partially regenerated adsorbent, the process of each reactor comprising: a pre-cooling step before said cooling step (c), wherein said partially regenerated adsorbent is contacted with a waste stream depleted of the target component which is provided by at least one other reactor of said plurality of reactors while performing the adsorption step (a), wherein a second amount of target component is desorbed providing a second output stream containing the target component; a pre-heating step after said adsorption step (a) and before said heating step (b), wherein said loaded adsorbent is contacted with a rinse stream containing the target component which is provided by at least one other reactor of said plurality of reactors while performing the pre-cooling step, wherein an amount of target component contained in said rinse stream is adsorbed and a second waste stream depleted of the target component is produced, wherein a first reactor provides said waste stream for the pre-cooling step, and a second reactor provides said rinse stream for the pre-heating step. (a) an adsorption step, comprising contacting an input stream of said gaseous mixture with a solid adsorbent and adsorption of target component from said input stream, providing a target component-loaded adsorbent and a first waste stream depleted of the target component; (b) heating of said loaded adsorbent and desorption of a first amount of target component, providing a partially regenerated adsorbent and a first output stream containing the desorbed target component; (c) cooling of said at least partially regenerated adsorbent, a pre-cooling step before said cooling step (c), wherein said partially regenerated adsorbent is contacted with a waste stream depleted of the target component which is provided by at least one other reactor of said plurality of reactors while performing the adsorption step (a), wherein a second amount of target component is desorbed providing a second output stream containing the target component; a pre-heating step after said adsorption step (a) and before said heating step (b), wherein said loaded adsorbent is contacted with a rinse stream containing the target component which is provided by at least one other reactor of said plurality of reactors while performing the pre-cooling step, wherein an amount of target component contained in said rinse stream is adsorbed and a second waste stream depleted of the target component is produced, wherein a first reactor provides said waste stream for the pre-cooling step, and a second reactor provides said rinse stream for the pre-heating step.