The invention relates to boiler adsorbers (1) for sorption apparatus packed with a solid, porous sorbent (2). The sorbent (2) exothermally sorbs a working medium in the vapour form. The boiler adsorber is fitted with a heat exchanger (3) which is flooded from below with a liquid heat transfer medium (4). By vaporisation, the heat transfer medium (4) removes heat from the sorbent 2 progressively from the bottom to the top, while the working medium flows from the top downwards into the sorbent packing and is sorbed in the sorbent (2). <IMAGE>