A thermal probe penetrating a glacier requires heat at the hot point for melting as well as along its entire length to balance the radial heat dissipation in the ice and thus prevent freezing in. The heat transfer problem is solved with a LaPlace transform and the results are developed graphically to simplify the numerical calculations. A performance diagram, developed as a design and operating aid, serves for analysis of the anticipated penetration performance of the probe and the required power levels. (Author).