Large Language Models (LLMs) have demonstrated remarkable performance across a wide range of natural language processing tasks. However, temporal reasoning, particularly under complex temporal constraints, remains a major challenge. To this end, existing approaches have explored symbolic methods, which encode temporal structure explicitly, and reflective mechanisms, which revise reasoning errors through multi-step inference. Nonetheless, symbolic approaches often underutilize the reasoning capabilities of LLMs, while reflective methods typically lack structured temporal representations, which can result in inconsistent or hallucinated reasoning. As a result, even when the correct temporal context is available, LLMs may still misinterpret or misapply time-related information, leading to incomplete or inaccurate answers. To address these limitations, in this work, we propose Neuro-Symbolic Temporal Reasoning (NeSTR), a novel framework that integrates structured symbolic representations with hybrid reflective reasoning to enhance the temporal sensitivity of LLM inference. NeSTR preserves explicit temporal relations through symbolic encoding, enforces logical consistency via verification, and corrects flawed inferences using abductive reflection. Extensive experiments on diverse temporal question answering benchmarks demonstrate that NeSTR achieves superior zero-shot performance and consistently improves temporal reasoning without any fine-tuning, showcasing the advantage of neuro-symbolic integration in enhancing temporal understanding in large language models.