The Greenland ice sheet has experienced significant melt over the past 6 decades, with extreme melt events covering large areas of the ice sheet. Melt events are typically analysed using summary statistics, but the nature and characteristics of the events themselves are less frequently analysed. Our work examines melt events from a statistical perspective by modelling 19 years of Moderate Resolution Imaging Spectroradiometer (MODIS) ice surface temperature data using a Gaussian mixture model. We use a mixture model with separate model components for ice and meltwater temperatures at 1139 cells spaced across the ice sheet. By considering the uncertainty in the ice surface temperature measurements, we use the two categories of model components to define, for each observation, a probability of melt which is independent of any pre-defined fixed melt threshold. This probability can then be used to estimate the expected number of melt events at a given cell. Furthermore, the model can be used to estimate temperature quantiles at a given cell and analyse temperature and melt trends over time by fitting the model to subsets of time. Fitting the model to data from 2001–2009 and 2010–2019 shows increases in melt probability and yearly expected maximum temperatures for significant portions of the ice sheet.