In recent years, knowledge graphs (KGs)–based question answering (QA) systems have significantly advanced in knowledge graph reasoning (KGR). However, real-world knowledge is often time-sensitive, which has made temporal knowledge graph question answering (TKGQA) an increasingly important topic in the research of temporal knowledge graphs (TKG). The core task of TKGQA is to retrieve specific entities or timestamps from TKGs to answer temporal-related questions. Currently, the main challenge in TKGQA is dealing with temporal problems that involve complex entities and temporal relationships. Existing methods are primarily limited to semantic parsing or temporal matching, making it difficult to effectively address such complex scenarios. To address this, we propose TCS-QA, a novel TKGQA method based on time constraints subgraphs and information fusion. Specifically, we introduce the auxiliary task of temporal order guidance in the temporal knowledge graph embedding (TKGE) to make the timestamp embedding time-sequence-aware. Additionally, in the subgraph extraction, subgraph pruning is performed using time constraints, and a temporal graph neural network (T-GNN) is employed to convey subgraph structural information. Subsequently, in the information fusion, a Transformer encoder is employed to effectively integrate the embedding information from the TKG and the problem context encoded by the pre-trained language models (PLMs), thereby deepening the understanding of the problem. Finally, the final answer is obtained in the answer prediction. Extensive experiments on two benchmark datasets show that TCS-QA significantly outperforms existing state-of-the-art models, particularly when dealing with problems involving complex entity structures and temporal information.