Facts change over time, making it essential for Large Language Models (LLMs) to handle time-sensitive factual knowledge accurately and reliably. Although factual Time-Sensitive Question-Answering (TSQA) tasks have been widely developed, existing benchmarks often face manual bottlenecks that limit scalable and comprehensive TSQA evaluation. To address this issue, we propose TDBench, a new benchmark that systematically constructs TSQA pairs by harnessing temporal databases and database techniques, such as temporal functional dependencies, temporal SQL, and temporal joins. We also introduce a new evaluation metric called time accuracy, which assesses the validity of time references in model explanations alongside traditional answer accuracy for a more fine-grained TSQA evaluation. Extensive experiments on contemporary LLMs show how TDBench enables scalable and comprehensive TSQA evaluation while reducing the reliance on human labor, complementing current TSQA evaluation approaches that largely center on Wikipedia/Wikidata by enabling LLM evaluation on application-specific data.