Facts extraction is pivotal for constructing knowledge graphs. Recently, the increasing demand for temporal facts in downstream tasks has led to the emergence of the task of temporal fact extraction. In this paper, we specifically address the extraction of temporal facts from natural language text. Previous studies fail to handle the challenge of establishing time-to-fact correspondences in complex sentences. To overcome this hurdle, we propose a timeline-based sentence decomposition strategy using large language models (LLMs) with in-context learning, ensuring a fine-grained understanding of the timeline associated with various facts. In addition, we evaluate the performance of LLMs for direct temporal fact extraction and get unsatisfactory results. To this end, we introduce TSDRE, a method that incorporates the decomposition capabilities of LLMs into the traditional fine-tuning of smaller pre-trained language models (PLMs). To support the evaluation, we construct ComplexTRED, a complex temporal fact extraction dataset. Our experiments show that TSDRE achieves state-of-the-art results on both HyperRED-Temporal and ComplexTRED datasets.