Climate change discourse has expanded substantially in recent decades, yet computational analyses remain concentrated on high-resource languages. In this paper, we construct a longitudinal Vietnamese climate news corpus and examine thematic structure and temporal evolution in a lower-resource setting. The corpus comprises 10,401 articles published between 2004 and 2026 and is systematically preprocessed using linguistically informed word segmentation. To ensure domestic relevance, we apply transformer-based Named Entity Recognition and construct a geographically grounded subset of 4,501 Vietnam-focused documents. We analyze this dataset using both Latent Dirichlet Allocation and BERTopic. Results reveal stable thematic dimensions alongside longitudinal shifts from event-driven pollution reporting toward governance- and energy-centered narratives. Embedding-based modeling achieves higher semantic coherence while maintaining comparable topic diversity. The main contribution of this work is thus the compilation of a structured Vietnamese climate corpus and a systematic analysis of discourse evolution in an underrepresented language context.