The impacts of heat waves in a warming climate depend not only on changing temperatures but also on changing humidity. Using 35 simulations from the Community Earth System Model Large Ensemble (CESM LENS), we investigate the long-term evolution of the joint distribution of summer relative humidity (RH) and daily maximum temperature (Tmax) near four U.S. cities (New York City, Chicago, Phoenix, and New Orleans) under the high-emissions Representative Concentration Pathway (RCP) 8.5. We estimate the conditional quantiles of RH given Tmax with quantile regression models, using functions of temperature for each city in July for three time periods (1990–2005, 2026–2035, and 2071–2080). Quality-of-fit diagnostics indicate that these models accurately estimate conditional quantiles for each city. As expected, each quantile of Tmax increases from 1990–2005 to 2071–2080, while mean RH decreases modestly. Conditional upon a fixed quantile of Tmax, the median and high quantiles of RH decrease, while those of the Heat Index (HI) and dew point both increase. This result suggests that, despite a modest decrease in median relative humidity, heat stress measured by metrics considering both humidity and temperature in a warming climate will increase faster than that measured by temperatures alone would indicate. For a fixed Tmax, the high quantiles of RH (and thus of HI and dew point) increase from 1990–2005 to 2071–2080 in all four cities. This result suggests that the heat stress of a day at a given Tmax will increase in a warming climate due to the increase of RH.