Vision-language models (VLMs) such as CLIP achieve strong zero-shot recognition but degrade significantly under \textit{temporally evolving distribution shifts} common in real-world scenarios (e.g., gradual illumination or seasonal changes). Existing continual test-time adaptation (CTTA) methods are typically built around sudden and severe distribution shifts and neglect temporal continuity, leading to three core defects: limited memory cache restricts long-range distribution modeling, causing catastrophic forgetting; entropy-based confidence becomes unreliable under temporal drift, worsening error accumulation; and static visual representations misalign with evolving inputs. We formalize this practical problem as \textit{Continual-Temporal Test-Time Adaptation (CT-TTA)}, where test distributions evolve gradually over time. To address it, we propose \textit{BayesTTA}, a Bayesian adaptation framework that enforces temporally consistent predictions and dynamically aligns visual representations. Specifically, BayesTTA incrementally estimates class-conditional Gaussian mixture distributions without storing raw data, adaptively selects covariance structures through statistical hypothesis testing, and performs calibrated inference using Gaussian discriminant analysis (GDA). These calibrated predictions supervise self-paced adaptation of normalization layers, ensuring efficient and stable representation alignment. We establish a comprehensive CT-TTA benchmark across four temporally evolving datasets and further evaluate generalization on ten standard TTA datasets. Extensive experiments show that BayesTTA consistently outperforms state-of-the-art methods, achieving significant gains while maintaining efficiency. Code is available at \href{https://github.com/cuishuang99/BayesTTA}{https://github.com/cuishuang99/BayesTTA}.