Thermal runaway in lithium-ion batteries poses a major safety challenge as the demand for higher energy density and larger battery packs continues to grow. This study presents a numerically stable finite element framework for simulating the initiation and propagation of thermal runaway events in lithium-ion cells. The governing heat transfer and reaction kinetics equations are reformulated in logarithmic space to mitigate numerical stiffness caused by exponential reaction rate dependencies, enabling efficient time integration across multiple scales. A Galerkin/Gradient-Least-Squares (GGLS) stabilization scheme is incorporated to suppress spurious oscillations arising from strongly reactive source terms, ensuring robust performance even under extreme thermal conditions. The model is further extended with a venting formulation that provides an estimation of gas generation and mass loss following cell rupture, providing a realistic representation of post-venting cooling behavior. Validation against experimental data from pouch cell heating tests and module-level thermal propagation demonstrates strong agreement in onset temperature, reaction progression, and transient cooling after venting. The proposed framework offers a scalable and physically consistent computational tool for studying cell-to-cell thermal propagation, improving thermal management design, and enhancing battery safety. Because the model relies on experimentally derived input data, it can be naturally extended to include the effects of cell aging and state of charge.