Method of operating an adsorption compressor system, which system comprises a hot source and a cold source and at least a first and a second adsorption bed, wherein the first bed has an initial temperature that is lower than the initial temperature of said second bed, in which system heat is circulated using a heat transfer fluid, the method being characterised in that it comprises the following phases: phase A) comprising the steps of: - heating the first adsorption bed by feeding HTF to it, coming from said second bed, via said hot source, while maintaining a thermal wave in said first bed; and - cooling the second adsorption bed by feeding HTF to it, coming from said first bed, via said cold source, while maintaining a thermal wave in said second bed; wherein phase A) is maintained until the exit temperature of said first bed and said second bed are essentially the same and phase B) comprising the steps of: - feeding the HTF effluent of said first bed to said hot source and from said hot source back into said first bed; and - feeding the HTF effluent of said second bed to said cold source and from said cold source back into said second bed; wherein phase B) is maintained until the temperature in said first bed is essentially homogeneous and the temperature in said second bed is also essentially homogeneous and lower than the temperature of said first bed, wherein the flow rates of said HTF through said first and second bed may be higher than in phase A). phase A) comprising the steps of: - heating the first adsorption bed by feeding HTF to it, coming from said second bed, via said hot source, while maintaining a thermal wave in said first bed; and - cooling the second adsorption bed by feeding HTF to it, coming from said first bed, via said cold source, while maintaining a thermal wave in said second bed; wherein phase A) is maintained until the exit temperature of said first bed and said second bed are essentially the same - heating the first adsorption bed by feeding HTF to it, coming from said second bed, via said hot source, while maintaining a thermal wave in said first bed; and - cooling the second adsorption bed by feeding HTF to it, coming from said first bed, via said cold source, while maintaining a thermal wave in said second bed; wherein phase A) is maintained until the exit temperature of said first bed and said second bed are essentially the same and phase B) comprising the steps of: - feeding the HTF effluent of said first bed to said hot source and from said hot source back into said first bed; and - feeding the HTF effluent of said second bed to said cold source and from said cold source back into said second bed; wherein phase B) is maintained until the temperature in said first bed is essentially homogeneous and the temperature in said second bed is also essentially homogeneous and lower than the temperature of said first bed, wherein the flow rates of said HTF through said first and second bed may be higher than in phase A). - feeding the HTF effluent of said first bed to said hot source and from said hot source back into said first bed; and - feeding the HTF effluent of said second bed to said cold source and from said cold source back into said second bed; wherein phase B) is maintained until the temperature in said first bed is essentially homogeneous and the temperature in said second bed is also essentially homogeneous and lower than the temperature of said first bed, wherein the flow rates of said HTF through said first and second bed may be higher than in phase A).