An effect previously discussed by Duley (1973) and by Greenberg and Hong (1974) is analyzed in detail. If an interstellar grain as small as 0.005 micron in diameter absorbs a starlight photon or is struck by a low-energy cosmic ray, its temperature must abruptly rise by some tens of degrees. The temperature-time curves for such grains in a typical unshielded environment are derived. Whether the temperature fluctuations can prevent growth of a grain mantle depends on the energy with which accreting material is bound. The results suggest that if the binding energy is as small as 0.1 eV, a mantle will evaporate even if its radius is as large as 0.01 micron, while a binding energy as large as 0.3 eV would allow accretion onto a grain with a radius as small as 0.005 micron.