An apparatus for heating or evaporating liquids or gases in which a homogeneous gaseous mixture of fuel and oxidizing agent is passed through a gas-permeable bed of a radiation substance, in which it undergoes flameless combustion with an extremely high intensity, so that the entire heat is converted into radiation emitted by the radiation substance. The radiation substance transmits heat in this form to a system of hollow jackets, which are preferably of cylindrical or prismatic formation, co-axially placed one inside the other so as to produce continuous annular spaces between neighbouring jackets, said spaces being filled with the radiation substance. The apparatus thereby disperses with surfaces for heat exchange by convection.