Context: Remote light scattering and thermal infrared observations provide clues about the physical properties of cometary and interplanetary dust particles. Identifying these properties will lead to a better understanding of the formation and evolution of the Solar System. Aims: We present a numerical solution for the radiative and conductive heat transport in a random particulate medium enclosed by an arbitrarily shaped surface. The method will be applied to study thermal properties of cometary dust particles. Methods: The recently introduced incoherent Monte Carlo radiative transfer method developed for scattering, absorption, and propagation of electromagnetic waves in dense discrete random media is extended for radiative heat transfer and thermal emission. The solution is coupled with the conductive Fourier transport equation that is solved with the finite-element method. Results: The proposed method allows the synoptic analysis of light scattering and thermal emission by large cometary dust particles consisting of submicrometer-sized grains. In particular, we show that these particles can sustain significant temperature gradients resulting in the superheating factor phase function observed for the coma of comet 67P/Churyumov-Gerasimenko.
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