Multifunctional vibroacoustic devices that tailor energy transmission under changing environmental conditions are of increasing interest for noise and vibration control. Phase change materials (PCMs) are promising for such applications because their mechanical properties change substantially across solid-liquid transitions, which enables temperature-dependent tuning [1]. However, inverse design studies that systematically exploit temperature-dependent PCM properties to achieve temperature-selective control of both acoustic transmission and structural vibration transmission remain limited, particularly for monolithic coupled acoustic-structural systems. To address this, we propose a density-based topology optimization framework for PCM-embedded structures that realize distinct transmission characteristics at prescribed temperature states. The optimization problem is formulated to promote thermally switchable performance by leveraging the temperature-dependent material property contrast of the PCM. The design is represented using a density-based method on a fixed background mesh, where filtering and projection are employed to obtain stable and near-binary material distributions. The coupled response is evaluated using a mixed displacement-pressure (u/p) finite element formulation, which provides a unified treatment of the coupled interface conditions without explicit interface reconstruction [2]. Numerical examples demonstrate temperature-selective transmission performance in both the acoustic and vibration regimes, illustrating the feasibility of topology-optimized PCM-embedded vibroacoustic systems for thermally tunable multifunctional transmission control.