Changes in the timescales at which complex systems evolve are essential to predicting critical transitions and catastrophic failures. Disentangling the timescales of the dynamics governing complex systems remains a key challenge. With this study, we introduce an integrated Bayesian framework based on temporal network models to address this challenge. We focus on two methodologies: change point detection for identifying shifts in system dynamics, and a spectrum analysis for inferring the distribution of timescales. Applied to synthetic and empirical datasets, these methologies robustly identify critical transitions and comprehensively map the dominant and subsidiaries timescales in complex systems. This dual approach offers a powerful tool for analyzing temporal networks, significantly enhancing our understanding of dynamic behaviors in complex systems.