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Abstract We quantify the skill of Coupled Model Intercomparison Project Phase 5 (CMIP5) and CMIP6 models to represent daily temperature extremes. We find CMIP models systematically exaggerate the magnitude of daily temperature anomalies for both cold and hot extremes. We assess the contribution to a daily temperature extreme from four terms: the long‐term mean annual cycle, the diurnal cycle, synoptic variability, and seasonal variability for both cold and hot extremes. These four terms are combined, and the overall performance of individual climate models assessed. This identifies those models that can simulate temperature extremes well and simulate them well for the right reasons. The new error metric shows that increases in horizontal resolution usually lead to a better performance particularly for the coarser resolution models. The CMIP6 improvements relative to CMIP5 are systematic across most land regions and are only partially explained by the increase in horizontal resolution, and other differences must therefore help explain the higher CMIP6 skill. , Key Points CMIP5 and CMIP6 models exaggerate the magnitude of daily temperature anomalies for hot days and cold nights extremes Higher‐resolution models improve the simulation of temperature extremes largely due to better simulation of synoptic scales CMIP6 outperforms the simulation of temperature extremes compared to CMIP5 beyond the benefits given by the higher resolution