Thermal cycling environments are common in engineering applications such as engines, electronic components, and additive manufacturing processes. Under thermal cycling conditions, materials repeatedly expand and contract, generating residual stresses. Although thermal-crystal plasticity simulations provide a powerful framework for capturing coupled thermal-mechanical phenomena at the crystal grain scale, the influence of thermal cycle frequency on the spatiotemporal evolution of stress within polycrystalline materials remains unclear. This limitation is partly due to the lack of systematic post-processing methods capable of simultaneously capturing spatial heterogeneity and temporal evolution. In this study, we investigate the effect of thermal cycle frequency on polycrystalline-scale stress responses using coupled thermal-crystal plasticity finite element simulations. Periodic thermal loading with different cycle frequencies is applied to a polycrystalline model, and the resulting evolution of the von Mises stress field is analysed. To extract the dominant spatiotemporal structures embedded in the high-dimensional simulation data, dynamic mode decomposition (DMD) is employed as a diagnostic and data-driven analysis tool. The results reveal a clear transition in stress response behaviour with increasing thermal cycle frequency. Under low-frequency conditions, the stress field exhibits a quasi-steady, periodic response synchronized with the imposed thermal cycle, dominated by modes with near-zero growth rates. In contrast, high-frequency thermal cycling induces inharmonic and non-steady stress responses characterized by multiple interacting modes with nonzero growth or decay rates, reflecting strong history-dependent and transient behaviour. The DMD analysis successfully identifies these frequency-dependent modal structures and enables low- dimensional reconstruction of the stress evolution. These findings demonstrate that DMD provides a systematic framework for interpreting complex thermal-mechanical responses in polycrystalline materials. The proposed approach offers new insights into how thermal cycle frequency governs the temporal structure of plastic response and provides a promising tool for analysing thermal fatigue phenomena under rapid or cyclic thermal loading.