The continued use of the Positive Degree-Day (PDD) method to predict ice sheet melt is generally favoured over surface energy balance methods partly due to the computational efficiency of the algorithm and the requirement of only one input variable (temperature). In this paper we revisit some of the assumptions governing the application of the PDD method. Using hourly temperature data from the GC-Net network we test the assumption that monthly PDD total (PDDm) can be represented by a Gaussian distribution with fixed standard deviation of monthly temperature (σM). The results presented here show that the common assumption of fixed σM does not hold, and that σM may be represented more accurately as a quadratic function of average monthly temperature. For Greenland, the mean absolute error in predicting PDDm using our methodology is 3.9°C*day, representing a significant improvement on current methods (7.8°C*day, when σM = 4.5°C). Over a range of glaciated settings, our method reproduces PDDm, on average, to within 1.5 - 8.5°C*day, compared to 4.4 - 15.7°C*day when σM = 4.5°. The improvement arises because we capture the systematic reduction in temperature variance that is observed over melting snow and ice, when surface temperatures cannot warm above O°C.