Statistical extreme value models allow estimation of the frequency, magnitude, and spatio-temporal extent of extreme temperature events in the presence of climate change. Unfortunately, the assumptions of many standard methods are not valid for complex environmental data sets, with a realistic statistical model requiring appropriate incorporation of scientific context. We examine two case studies in which the application of routine extreme value methods result in inappropriate models and inaccurate predictions. In the first scenario, incorporating random effects reflects shifts in unobserved climatic drivers that led to record-breaking US temperatures in 2021, permitting greater accuracy in return period prediction. In scenario two, a Gaussian mixture model fit to ice surface temperatures in Greenland improves fit and predictive abilities, especially in the poorly-defined upper tail around 0∘C.