Abstract: A gas separation process in which the thermal storage of the heat in the gas is desired as well as the gas separation. This invention outlines a novel process and system whereby the thermal storage efficiency can be vastly increased by matching the gas sorption fronts and the thermal fronts to cause thermal front sharpening. The gas separation process and system include an adsorption vessel having an adsorbent in an amount of 10-40% and a thermal storage component in an amount of 50-90% by volume.