Glacial lake‐moraine dam systems are widespread in cold alpine environments such as the Qinghai‐Tibet Plateau (QTP). Without climate change, the lake‐dam system exhibits stably dynamic evolution on a hydrological annual cycle. However, climate change may drive subtle alterations in the system's evolution. We developed a fully coupled Thermal‐Hydraulic‐Mechanical simulation platform considering ice‐water phase change, showing robust performance under CMIP6‐derived boundary conditions. Using this platform, we simulated climate warming‐driven multiphysics responses and dam stability evolutions of a homogeneous, simplified conceptual model of the lake‐dam system. We identified critical temperature thresholds for permanently frozen area thawing and abrupt changes in dam stability of this lake‐dam system. Considering the current slope stability situations on the QTP, the SSP 5–8.5 climate warming scenario is conservatively anticipated to pose significant geological safety risks due to potential disaster chains from glacial lake failures. Our study provides insights into profound geological process evolutions driven by climate change.