  In circumstellar disks or shells it is often assumed that gas and dust
temperatures are equal where the latter is determined by radiative equilibrium.
This paper deals with the question whether this assumption is applicable for
tenous circumstellar disks around young A stars. In this paper the thin
hydrostatic equilibrium models described by Kamp & Bertoldi (2000) are combined
with a detailed heating/cooling balance for the gas. The most important heating
and cooling processes are heating through infrared pumping, heating due to the
drift velocity of dust grains, and fine structure and molecular line cooling.
Throughout the whole disk gas and dust are not efficiently coupled by
collisions and hence their temperatures are quite different. Most of the gas in
the disk models considered here stays well below 300 K. In the temperature
range below 300 K the gas chemistry is not much affected by T_gas and therefore
the simplifying approximation T_gas = T_dust can be used for calculating the
chemical structure of the disk. Nevertheless the gas temperature is important
for the quantitative interpretation of observations, like fine structure and
molecular lines.
