  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.
