A method for drilling a geothermal well in a subterranean zone includes drilling, with a drill string, a wellbore of the geothermal well in the subterranean zone. An inherent temperature of the rock adjacent a rock face at a downhole end of the wellbore is at least 250 degrees Celsius. While drilling, a drilling fluid is flowed at a temperature at the rock face such that a difference between the inherent temperature of the rock adjacent the rock face and the temperature of the drilling fluid at the rock face is at least 100 degrees Celsius.