In order to assess the thermal stability of polar ice deposits, we present model calculated temperatures of flat surfaces and surfaces within bowl-shaped and flat-floored polar impact craters on Mercury and the Moon. Our model includes appropriate insolation cycles, realistic crater shapes, multiple scattering of sunlight and infrared radiation, and depth-and temperature-dependent regolith thermophysical properties. Unshaded water ice deposits on the surface of either body are rapidly lost to thermal sublimation. A subsurface water ice deposit is stable within 2 โข latitude of the Moon's poles. Meter-thick water ice deposits require billions of years to sublime if located in the permanently shaded portions of flat-floored craters within 10 โข latitude of the poles of Mercury and 13 โข latitude of the poles of the Moon. Results for craters associated with radar features on Mercury are consistent with the presence of stable water ice deposits if a thin regolith layer thermally insulates deposits at lower latitudes and within smaller craters. A regolith cover would also reduce losses from diffusion, ion sputtering, impact vaporization, and H Lyฮฑ and is implied independently by the radar observations. Permanently shaded areas near the Moon's poles are generally colder than those near Mercury's poles, but the Moon's obliquity history, its orbit through Earth's magnetospheric tail, and its radar-opaque regolith may limit the volume and radar detectability of ice deposits there.