Community search in heterogeneous information networks (HINs) often neglects temporal dynamics, yielding structures that poorly reflect real-world interactions. We introduce the Temporal HIN Community Search (THCS) problem and propose a novel (k, Tq, Pδ)-core model that captures both structural cohesiveness and temporal relevance. Our model uses a time span constraint δ to ensure interaction recency and a query interval Tq for flexible temporal exploration, filtering irrelevant connections while preserving structural density. We develop two efficient online algorithms—Center-based Sliding Window search and Incremental Center Expansion—that exploit meta-path symmetry and dynamic connectivity tracking. For frequent queries, we design a Temporal HIN Core Interval-Index (TCI-Index), organising minimal core intervals hierarchically with innovative compression techniques. Experiments on real-world datasets show our methods significantly outperform baselines, finding temporally meaningful communities with high efficiency.