The human impacts of changes in heat events depend on changes in the joint behavior of temperature and humidity. Little is currently known about these complex joint changes, either in observations or projections from general circulation models (GCMs). Further, GCMs do not fully reproduce the observed joint distribution, implying a need for simulation methods that combine information from GCMs with observations for use in impact studies. We present an observation-based, conditional quantile mapping approach for the simulation of future temperature and humidity. A temperature simulation is first produced by transforming historical temperature observations to include projected changes in the mean and temporal covariance structure from a GCM. Next, a humidity simulation is produced by transforming humidity observations to account for projected changes in the conditional humidity distribution given temperature, using a quantile regression model. We use the Community Earth System Model Large Ensemble (CESM1-LE) to estimate future changes in summertime (June - August) temperature and humidity over the Continental United States (CONUS), and then use the proposed method to create future simulations of temperature and humidity at stations in the Global Summary of the Day dataset. We find that CESM1-LE projects decreases in summertime humidity across CONUS for a given deviation in temperature from the forced trend, but increases in the risk of high dewpoint on historically hot days. In comparison with raw CESM1-LE output, our observation-based simulation largely projects smaller changes in the future risk of either high or low humidity on days with historically warm temperatures.