A large class of bodies in the solar system consists of ices mixed wit
h ''dusty'' or ''rocky'' material (e.g., comets, rings, icy satellites
). In the present paper we study the thermal behavior of such a mixed
body in response to irradiation by the Sun, In contrast to the traditi
onal approach, where the effects of a dust mantle are considered from
a macroscopic point of view, we focus on the behavior of single grains
or boulders. A three-dimensional model for a dust particle, or a piec
e of refractory dark material in contact with a volatile ice surface,
is presented. Example solutions are calculated, which illustrate the i
nfluence of different heat transfer paths (radiation, conduction), the
particle size, and the contact area (Hertz factor) upon the solutions
. Subsequently, our model is used to interpret some results of a recen
t comet simulation experiment, and, finally, it is applied to estimate
the temperature contrasts on the surface of the icy satellites of Jup
iter and Saturn.