Abstract The existence of nonvolatile dust mantles covering the ices of cometary nuclei is suggested both from the behavior of many cometary lightcurves and from the direct observations of Comet Halley's nucleus by the Giotto and VEGA spacecraft in March 1986. In this paper we present a systematic study which sheds some light on the evolution of such dust-ice systems when they are irradiated by the sun. Hereby we assume that the dust mantle as well as the underlying ice are grainy, porous structures permeable to gases. It is found that both the surface temperature of the dust mantle and the temperature at the dust-ice interface are strong functions of the average pore radius of the materials and of the thermal conductivity of the mantle. For moderately insulating dust mantles (coal dust) with grain sizes in the micrometer range, high ice temperatures (up to the triple point of water ice) may be reached in response to irradiation with one solar constant. If the dust mantles are extremely bad heat conductors (assuming radiative heat transfer only) the ice temperature remains below 200 K in all cases considered. An increase of the dust mantle thickness may result either in a higher or in a lower ice temperature, depending upon the parameters chosen.