Thermal drilling has been applied to studies of glaciers on Earth and proposed for study of the martian ice caps and the crust of Europa. Additionally, inadvertent thermal drilling by radioisotope sources released from the breakup of a space vehicle is of astrobiological concern in that this process may form a downward-propagating "warm little pond" that could convey terrestrial biota to a habitable environment. A simple analytic solution to the asymptotic slow-speed case of thermal drilling is noted and used to show that the high thermal conductivity of the low-temperature ice on Europa and Titan makes thermal drilling qualitatively more difficult than at Mars. It is shown that an isolated General Purpose Heat Source (GPHS) "brick" can drill effectively on Earth or Mars, whereas on Titan or Europa with ice at 100 K, the source would stall and become stuck in the ice with a surface temperature of <200 K.