Identifying communities from temporal networks facilitates the understanding of potential dynamic relationships among entities, which has already received extensive applications. However, existing methods primarily rely on lower-order connectivity (e.g., temporal edges) to capture the structural and temporal cohesiveness of the community, often neglecting higher-order temporal connectivity, which leads to sub-optimal results. To overcome this dilemma, we propose a novel temporal community model named maximal-truss (MDT). This model emphasizes maximal temporal support, ensuring all edges are connected by a sequence of triangles with elegant temporal properties. To search the MDT containing the user-initiated query node q (q-MDT), we first design a powerful local search framework with some effective pruning strategies. This approach aims to identify the solution from the small temporal subgraph which is expanded from q. To further improve the performance on large graphs, we build the temporal trussness index (TT-index) for all edges. Leveraging the TT-index allows us to efficiently search high-probability target subgraphs instead of performing a full search across the entire input graph. Empirical results on nine real-world networks and seven competitors demonstrate the superiority of our solutions in terms of efficiency, effectiveness, and scalability