Hot-point drills have been widely used for drilling boreholes in glaciers, ice caps and ice sheets. A hot-point drill melts ice through the thermal head at its bottom end. Penetration occurs through a close-contact melting (CCM) process, in which the ice is melted, and the meltwater is squeezed out by the exerted force applied on the thermal head. During the drilling, a thin water film is formed to separate the thermal head from the surrounding ice. For the hot-point drill, the rate of penetration (ROP) is influenced by several variables, such as thermal head shape, buoyancy corrected force (BCF), thermal head power (or temperature) and ice temperature. In this study, we developed a model to describe the CCM process, where a constant power or temperature on the working surface of a thermal head is assumed. The model was developed using COMSOL Multiphysics 5.3a software to evaluate the effects of different variables on the CCM process. It was discovered that the effect of thermal head shape and the cone angle of conical thermal head on ROP is less significant, whereas the increase in the BCF and the power (or temperature) of the thermal head can continuously enhance the ROP.