Due to surface melting, meltwater lakes seasonally form on the surface of glaciers. These lakes drive hydrofractures that rapidly transfer water to the base of ice sheets. This paper presents a computational method to capture the complicated hydrofracturing process. Our work reveals that viscous ice rheology has a great influence on the short-term propagation of fractures, enabling fast lake drainage, whereas thermal effects (frictional heating, conduction, and freezing) have little influence.