Facts evolve over time, making it essential for Large Language Models (LLMs) to handle time-sensitive factual knowledge accurately and reliably. While factual Time-Sensitive Question-Answering (TSQA) tasks have been widely studied, existing benchmarks often rely on manual curation or a small, fixed set of predefined templates, which restricts scalable and comprehensive TSQA evaluation. To address these challenges, we propose TDBench, a new benchmark that systematically constructs TSQA pairs by harnessing temporal databases and database techniques such as temporal SQL and functional dependencies. We also introduce a fine-grained evaluation metric called time accuracy, which assesses the validity of time references in model explanations alongside traditional answer accuracy to enable a more reliable TSQA evaluation. Extensive experiments on contemporary LLMs show how \ours{} enables scalable and comprehensive TSQA evaluation while reducing the reliance on human labor, complementing existing Wikipedia/Wikidata-based TSQA evaluation approaches by enabling LLM evaluation on application-specific data and seamless multi-hop question generation. Code and data are publicly available at: https://github.com/ssoy0701/tdbench.git.