Using ensembles from the Community Earth System Model (CESM) under a high and a lower emission scenarios, we investigate changes in statistics of extreme daily temperature. The ensembles provide large samples for a robust application of extreme value theory. We estimate return values and return periods for annual maxima of the daily high and low temperatures as well as the 3-day averages of the same variables in current and future climate. Results indicate statistically significant increases (compared to the reference period of 1996–2005) in extreme temperatures over all land areas as early as 2025 under both scenarios, with statistically significant differences between them becoming pervasive over the globe by 2050. The substantially smaller changes, for all indices, produced under the lower emission case translate into sizeable benefits from emission mitigation: By 2075, in terms of reduced changes in 1-day heat extremes, about 95 % of land regions would see benefits of 1 °C or more under the lower emissions scenario, and 50 % or more of the land areas would benefit by at least 2 °C. 6 % of the land area would benefit by 3 °C or more in projected extreme minimum temperatures and 13 % would benefit by this amount for extreme maximum temperature. Benefits for 3-day metrics are similar. The future frequency of current extremes is also greatly reduced by mitigation: by the end of the century, under RCP8.5 more than half the land area experiences the current 20-year events every year while only between about 10 and 25 % of the area is affected by such severe changes under RCP4.5.