Hyper-arid deserts are traditionally viewed as thermodynamically uniform landscapes where extreme heat and chronic moisture deficits constrain biological persistence. However, this assumption overlooks localized land-atmosphere interactions that may create discrete islands of stability. Using high-resolution ERA5-Land reanalysis (2019-2024) across the Arabian Peninsula, we identify a Thermodynamic Decoupling Horizon at a mean Diurnal Temperature Range (DTR) of 12.0 degrees C, separating coastal advection from a radiation-dominated continental interior. Within this interior, we identify 109 spatially isolated thermodynamic refugia characterized by mean DTR values of 5.8 degrees C-substantially lower than the 14.0 degrees C observed in the surrounding Thermodynamic Void. These sites are maintained by a persistent nocturnal moisture pulse (similar to 44.1 g m(-2)) that enables morning evaporative buffering. Domain-wide scaling analysis (n = 5499) indicates that this buffering operates as a non-linear, threshold-dominated process (Spearman's rho = -0.68, p < 0.001), revealing an abrupt "hockey-stick" activation of thermal stability once critical moisture-coupling thresholds are exceeded. This mechanism truncates the high-temperature tail of the thermal distribution, reducing exposure to lethal heat stress (>35 degrees C) from 28.3% of total hours in the background desert to only 0.6% within refugia. Our findings demonstrate that habitability in extreme environments is governed primarily by the non-linear suppression of thermal extremes, rather than by moderation of mean temperatures. This framework provides a physics-informed basis for identifying climatically buffered habitats and guiding conservation strategies in the world's most extreme environments under accelerating climate change.