Summary: The problem of strong shock-wave propagation through a dust-laden gas is studied as a limiting case of very intensive heat transfer. According to a potential law, the variable energy input is continuously supplied by a driving piston or a surface. A self-similar solution is found under isothermal condition of the flow field. The spherical case is worked out in detail to investigate to what extent the shock wave is influenced by the energy input as well as by the mass concentration of the solid particles in the medium and the ratio of density of the solid particles to the initial density of the medium. Three different cases are covered with respect to parameters describing the increase of energy or the piston velocity: One corresponds to a decelerated piston, the second to a constant piston velocity and the third to a continuously accelerated piston starting from rest. The dust-free flow is included in the numerical results as a limiting case.