Temporal Sentence Grounding (TSG), which aims to localize moments from videos based on the given natural language queries, has attracted widespread attention. Existing works are mainly designed for short videos, failing to handle TSG in long videos, which poses two challenges: i) complicated contexts in long videos require temporal reasoning over longer moment sequences, and ii) multiple modalities including textual speech with rich information require special designs for content understanding in long videos. To tackle these challenges, in this work we propose a Grounding-Prompter method, which is capable of conducting TSG in long videos through prompting LLM with multimodal information. In detail, we first transform the TSG task and its multimodal inputs including speech and visual, into compressed task textualization. Furthermore, to enhance temporal reasoning under complicated contexts, a Boundary-Perceptive Prompting strategy is proposed, which contains three folds: i) we design a novel Multiscale Denoising Chain-of-Thought (CoT) to combine global and local semantics with noise filtering step by step, ii) we set up validity principles capable of constraining LLM to generate reasonable predictions following specific formats, and iii) we introduce one-shot In-Context-Learning (ICL) to boost reasoning through imitation, enhancing LLM in TSG task understanding. Experiments demonstrate the state-of-the-art performance of our Grounding-Prompter method, revealing the benefits of prompting LLM with multimodal information for TSG in long videos.