Abstract: Heat exchanger for gases, comprising a vertical shaft with upward flow of gas between rows of staggered horizontally disposed sets of tubes, downwardly restricted by a gas penetrable bottom (2) and upwardly by the uppermost set of tubes, and over its entire vertical length containing a granular material (7) which is kept in motion by the essentially vertically upward gas stream. The heat exchanger is characterized therein that the ratio between the diagonal free opening a and the horizontal free opening b between the tubes (4) in the set of tubes lies within the range 0.45:1-0.9:1 for controlling and restricting the vertical movement of the grains in the heat exchanger, thereby obtaining an approximately continuous temperature gradient in the gas-grain mixture over the entire height of the heat exchanger.