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Regions of shorter-than-Gaussian warm-side temperature anomaly distribution tails are shown to occur in spatially coherent patterns in global reanalysis. Under such conditions, future warming may be manifested in more complex ways than if the underlying distribution were close to Gaussian. For example, under a uniform warm shift, the simplest prototype for future warming, a location with a short tail would experience a greater increase in extreme warm exceedances relative to a fixed threshold compared to if the distribution were Gaussian. The associated societal and environmental impacts make realistic representation of these short tails an important target for climate models. Global evaluation of the ability for a suite of global climate models (GCMs) contributing to phase 5 of the Coupled Model Intercomparison Project (CMIP5) suggests that most models approximately capture the principal observed coherent regions of short tails. This suggests the underlying dynamics and physics occur on scales resolved by the models, and helps build confidence in model simulations of extremes. Furthermore, most GCMs show more rapid future increases in exceedances of the historical 95th percentile in regions exhibiting short tails in the historical climate. These regions, where the ratio of exceedances projected by the GCM compared to that expected from a Gaussian sometimes exceeds 1.5, are termed hot spots. Prominent hot spots include western North America, Central America, a broad swath of northwestern Eurasia, and the Indochina Peninsula during boreal winter. During boreal summer, central and western Australia, parts of southern Africa, and portions of central South America are major hot spots.