This article examines the application of time-temperature superpositioning (TTS) in certain thermorheologically complex polymers using a recently developed phenomenological model that describes crosslinked polymer viscoelasticity based on fundamental physical considerations. The model＇s capability to calculate both isochronal temperature sweeps and isothermal frequency sweeps of storage and loss moduli allows us to simulate conditions typical of certain thermorheologically complex polymers. We use the model to generate modulus frequency sweeps over the Limited range of frequencies that are typically accessible to experiments. We apply TTS to shift these sweeps along the frequency axis to construct master curves. The model master curves are then compared with the model＇s "true" moduli curves over the full frequency domain at the reference temperature. This comparison suggests that nonsuperposability may go unnoticed if we only rely on the smoothness of the storage modulus master curve. Superpositioning to achieve a smooth loss modulus master curve tends to be more reliable. This has serious implications for assessing the reliability of relaxation moduli and creep compliance master curves that have no associated loss component that can be used to assess the quality of superpositioning.