PURPOSE: To reduce in size a cooler and to prevent slagging due to dust.

CONSTITUTION: A gas cooler introduces high temperature gas containing dusts, such as ash, etc., having adhesive properties into a gas introducing chamber 6 in a pressure vessel 3, passes it from the chamber 6 to outside of a heat transfer tube 9 through the tube 9 to heat exchange it with cooling medium, and partitions the chamber 6 by a protective wall (protective plate 13, a water- cooled wall 18) held at a surface at a temperature in which, even if dusts are collided, the dusts do not adhere.