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Abstract Vapor buildup in the atmosphere and faster warming over land than over ocean are ubiquitous features of climate change. This combination is a threat to society because the associated heat stress may exceed the limit for human survival. The heat stress due to high humidity and high temperature is quantified with the wet‐bulb temperature (Tw). A common view is that the land Tw should change at the same rate as the ocean surface temperature (Ts). Using climate model data and atmospheric observations, we show that the land Tw increases 17% faster than Ts. This amplification arises from stronger downward longwave radiation (L↓) at the surface in a warmer climate, which causes moist static energy to accumulate in the atmospheric boundary layer. We also find that L↓ is a better predictor of Tw than Ts at interannual to decadal time scales. These relationships are robust across climates and across model simulations.