A Temperature Swing Adsorption method for separating a first component, comprising a more adsorbable component, from a feed stream comprising more than 50 mol % of a second component, comprising a less adsorbable component, is provided. The method includes providing an adsorbent structure suitable for adsorbing the first component, the structure being of the parallel passage contactor type, and cyclically implementing the following steps. Passing the feed stream through the adsorbent structure thus adsorbing the first component and producing a stream depleted in the first component and enriched in the second component. Heating the adsorbent structure to desorb the adsorbed first component by means of circulating a heating stream enriched in the first component at a temperature suitable for regeneration. And cooling the structure by means of passing through it more than 50% of the stream enriched in the second component produced in the step a).