Abstract Environmental moist heat is a measure of the ability for humans to cool by evaporation. It is commonly quantified as “wet‐bulb temperature.” Extreme moist heat acts as an upper limit to human survivability. In the tropics, maximum moist heat in models is constrained via convective stability by the weak temperature gradient approximation combined with entraining quasi‐equilibrium dynamics. We examine how observed monthly maximum moist heat varies with atmospheric instability and dryness in comparison to reanalysis. In observations, extreme moist heat increases with lower‐tropospheric saturation deficit in convecting regions as expected from theory. However, weather stations show higher moist heat than reanalysis. We hypothesize that a combination of poor representation of convection sensitivity to lower tropospheric dryness and breakdown of quasi‐equilibrium on small scales causes the extremes in weather stations to be underpredicted by entraining quasi‐equilibrium dynamics calculated from reanalysis statistics. Allowing for small, positive instability better represents extremes.