The efficient simulation of damped wave propagation is critical in applications ranging from room acoustics to seismic analysis. Space-time domain decomposition methods, specifically Schwarz Waveform Relaxation (SWR), offer a powerful framework for parallelizing these problems. However, the convergence rate of SWR is heavily dependent on the choice of transmission conditions at the subdomain interfaces. While optimized conditions are well-established for the classical wave equation, applying these same conditions to problems with physical damping, specifically of viscoelastic and telegrapher types, is suboptimal, as the added dissipation introduces complex diffusive behavior that the standard wave conditions do not account for. This work presents a rigorous asymptotic framework to derive optimized Robin-type transmission conditions. We analyze the convergence factor in the frequency domain, addressing the full spectrum of physical behaviors generated by the interplay between frequency, damping intensity, and subdomain overlap. Our analysis derives optimal formulas for the coefficients of the transmission operator across limiting regimes, ranging from purely propagative behavior, where damping acts as a perturbation, to highly dissipative regimes where the physics becomes diffusion-dominated. We further investigate the influence of the overlap size, identifying a critical transition in the optimization landscape: the optimal strategy shifts from error equioscillation over a frequency band to targeted mode absorption as the overlap increases. Numerical experiments confirm that our asymptotically derived coefficients significantly accelerate convergence compared to using the standard transmission conditions optimized for the undamped wave equation, providing a robust and scalable solution for damped wave simulations.