<p>The Optimized Schwarz Waveform Relaxation (OSWR) method decomposes the heat-viscoelastic interaction model into two single physical processes, solved using existing numerical methods and coupled via transmission conditions to reconstruct system behavior. Efficient transmission conditions are critical for rapid convergence. In this study, we propose three Robin-type transmission conditions by relaxing interface coupling. For the standard Robin condition, convergence is rigorously proven via energy estimate. Fourier analysis further characterizes the convergence factor in the frequency domain, enabling optimization of relaxation parameters through asymptotic analysis and high-frequency approximations. Our results reveal, for the first time in multi-physics systems, that “heterogeneity” (thermal conductivity and damping coefficient contrast) significantly impacts OSWR’s performance. Specifically, higher “heterogeneity” accelerates convergence for both scaled and two-sided Robin conditions. Notably, the two-sided Robin OSWR is mesh-independent, depending solely on “heterogeneity”. Numerical experiments validate these theoretical findings.</p>