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Abstract The frequency of heat waves (defined as daily temperature exceeding the local 90th percentile for at least three consecutive days) during summer in the United States is examined for daily maximum and minimum temperature and maximum apparent temperature, in recent observations and in 10 CMIP5 models for recent past and future. The annual average percentage of days participating in a heat wave varied between approximately 2% and 10% in observations and in the model’s historical simulations during 1979–2005. Applying today’s temperature thresholds to future projections, heat-wave frequencies rise to more than 20% by 2035–40. However, given the models’ slight overestimation of frequencies and positive trend rates during 1979–2005, these projected heat-wave frequencies should be regarded cautiously. The models’ overestimations may be associated with their higher daily autocorrelation than is found in observations. Heat-wave frequencies defined using apparent temperature, reflecting both temperature and atmospheric moisture, are projected to increase at a slightly (and statistically significantly) faster rate than for temperature alone. Analyses show little or no changes in the day-to-day variability or persistence (autocorrelation) of extreme temperature between recent past and future, indicating that the future heat-wave frequency will be due predominantly to increases in standardized (using historical period statistics) mean temperature and moisture content, adjusted by the local climatological daily autocorrelation. Using nonparametric methods, the average level and spatial pattern of future heat-wave frequency is shown to be approximately predictable on the basis of only projected mean temperature increases and local autocorrelation. These model-projected changes, even if only approximate, would impact infrastructure, ecology, and human well-being.