This study presents a comprehensive reliability assessment of passive nuclear cooling systems exposed to corrosion in stratified high-temperature water environments. A surface chemistry–based corrosion model is developed, grounded in the Langmuir-Hinshelwood reaction mechanism, incorporating temperature-dependent adsorption and oxygen concentration effects. To account for thermal stratification, a novel analytical expression integrates average temperature and gradient-driven correction terms. The corrosion model is validated against empirical data for steel in hot water, demonstrating accurate capture of experimental trends. A reliability framework is constructed using a Weibull-based probabilistic approach, linking corrosion depth to structural failure criteria. A Monte Carlo uncertainty analysis is also conducted, quantifying the impact of parameter variability on failure probabilities over time. The results reveal that early-life failure risk is pivotal in high-temperature environments, emphasizing the importance of accurate degradation modeling for long-term system integrity.