A coupled finite-element and complex-eigenvalue model was established to investigate thermo-mechanically induced vibration in T-slot dry-gas seals during start-up and shutdown. The findings indicate that increasing thermal distortion tends to attenuate high-frequency instabilities, accentuate low-frequency modes, and narrow the overall stability margin. Within a multi-objective optimisation framework—combining sensitivity analysis with response-surface surrogates—the critical geometric parameters of the sealing ring were refined. The optimised design alleviated thermal distortion, reduced the prevalence of unstable modes, and improved equivalent damping characteristics, thereby mitigating friction-induced vibration. The proposed workflow may serve as a useful reference for designing more robust mechanical seals.