We calculated the temperatures of ice spheres in the mesosphere by establishing an equation for the balance among the power absorbed by the particle from the solar and terrestrial radiation fields, the power emitted by the particle as thermal radiation, and the power transferred from the particle to the atmosphere by collisions with air molecules. In some cases the particle temperature that ensues can result in a saturation vapor pressure at the ice surface that exceeds the pressure of the ambient atmosphere, and the particle can therefore not continue to exist. Equilibrium particle temperatures have been analyzed to study atmospheric exclusion limits for ice spheres in the mesosphere as a function of particle radius and altitude. *