A method of temperature swing adsorption allows separation of a first fluid component from a fluid mixture comprising at least the first fluid component in an adsorptive separation system having a parallel passage adsorbent contactor with parallel flow passages having cell walls which include an adsorbent material and axial thermally conductive filaments in direct contact with the adsorbent material. The method provides for transferring heat from the heat of adsorption in a countercurrent direction along at least a portion of the filaments during adsorption and transferring heat in either axial direction along the filaments to provide at least a portion of the heat of desorption during a desorption step. A carbon dioxide TSA separation process to separate carbon dioxide from flue gas also includes steps transferring heat from adsorption or for desorption along axial thermally conductive filaments.