A heat transfer apparatus (2) that uses an adsorbent material to generate a cooling effect. The heat transfer apparatus (2) includes a first vessel (4) containing adsorbent material (10) and a second vessel (6) interconnected to the first (4). A working substance is contained within the two interconnected vessels (4, 6). The adsorbent material (10) and working substance (26, 28) are sized such that the working substance is completely adsorbed in both liquid and solid states (26, 28) by the adsorbent material (10) from the second vessel (6) into the first (4), cooling the second vessel (6) and heating the first (4). Complete adsorption includes adsorption of the working substance by vaporization when the working substance is in a liquid phase (26) and adsorption by sublimation when the working substance is in a solid phase (28). The second vessel (6) contains a compressible foam which accommodates the expansion of the working substance when it changes phase from a liquid to a solid and prevents the second vessel (6) from breaking.
