  Context. While radiative cooling of interstellar grains is a well-known
process, little detail is known about the cooling of grains with an icy mantle
that contains volatile adsorbed molecules. Aims. We explore basic details for
the cooling process of an icy grain with properties relevant to dark
interstellar clouds. Methods. Grain cooling was described with a numerical code
considering a grain with an icy mantle that is structured in monolayers and
containing several volatile species in proportions consistent with interstellar
ice. Evaporation was treated as first-order decay. Diffusion and subsequent
thermal desorption of bulk-ice species was included. Temperature decrease from
initial temperatures of 100, 90, 80, 70, 60, 50, 40, 30, and 20K was studied,
and we also followed the composition of ice and evaporated matter. Results. We
find that grain cooling occurs by partially successive and partially
overlapping evaporation of different species. The most volatile molecules (N2)
first evaporate at the greatest rate and are most rapidly depleted from the
outer ice monolayers. The most important coolant is CO, but evaporation of more
refractory species, such as CH4 and even CO2, is possible when the former
volatiles are not available. Cooling of high-temperature grains takes longer
because volatile molecules are depleted faster and the grain has to switch to
slow radiative cooling at a higher temperature. For grain temperatures above
40K, most of the thermal energy is carried away by evaporation. Evaporation of
the nonpolar volatile species induces a complete change of the ice surface, as
the refractory polar molecules (H2O) are left behind. Conclusions. The
effectiveness of thermal desorption from heated icy grains (e.g., the yield of
cosmic-ray-induced desorption) is primarily controlled by the thermal energy
content of the grain and the number and availability of volatile molecules.
