A growing body of evidence indicates that anthropogenic greenhouse gases are changing Earth's climate, and that those changes may involve not only changes in climatic means but also in variability. Climate models may be informative about these future changes, but their use is complicated by the fact that they do not capture variability in current climate well. Many methods have therefore been developed to combine models and data in simulations of future climate, but current methods generally account only for changes in marginal variation and do not capture projected changes in correlation (spatial, temporal, spatiotemporal). We develop here a procedure to simulate future daily mean temperature that modifies climate observations based on changes in the mean and spectral density suggested by climate model output, and illustrate our methodology with projections from the CCSM3 (Community Climate System 3) climate model. We are able to simulate a future climate with changing temporal covariance while largely retaining non-Gaussian features of the observations. Our results suggest that in CCSM3, at most locations and most timescales, variability in daily mean temperature decreases under anthropogenic warming. The methodology presented here applies only to fully equilibrated future climate states, but may be extended to simulating transient states as well.