Network-based time series forecasting is a challenging task as it involves complex geometric properties, higher-order relations, and scale-free characteristics. Previous work has modeled network-based series as oversimplified graphs or has ignored the power law dynamics of real-world temporal and dynamic networks, which could yield suboptimal results. With the aim to address these issues, here we propose THINK, a novel framework based on hypergraph learning that captures the hyperbolic properties of time-evolving dynamic hypergraphs. We design an elegant hyperbolic distance-aware hypergraph attention mechanism to better capture informative internal structural features on the Poincaré ball. Through quantitative and conceptual analysis on seven tasks across temporal, and time-evolving dynamic hypergraphs, we demonstrate THINK's practicality in comparison to a variety of benchmarks spanning finance, health, and energy networks. © 2022 IEEE.