Recent radar observations of Mercury have revealed the presence of anomalous radar reflectivity and polarization features near its north and south poles. Thermal model calculations show that, despite Mercury's proximity to the sun, the temperatures of flat, low-reflectivity surfaces at Mercury's poles are not expected to exceed 167 kelvin. The locations of the anomalous polar radar features appear to be correlated with the locations of large, high-latitude impact craters. Maximum surface temperatures in the permanently shadowed regions of these craters are expected to be significantly colder, as low as 60 kelvin in the largest craters. These results are consistent with the presence of water ice, because at temperatures lower than 112 kelvin, water ice should be stable to evaporation over time scales of billions of years.