Modern IT systems generate vast amounts of log data, which pose challenges for Large Language Models (LLMs) due to their large size, irrelevant entries, and non-Natural Language (non-NL) construct (e.g., domain-specific jargon, error codes, file paths, and abbreviations). Traditional methods like Retrieval-Augmented Generation (RAG) and GraphRAG fail to preserve temporal sequences, handle non-NL for context and entities extraction, and dynamically prioritize query-relevant context. To address these limitations, we propose HG-InsightLog, a novel framework that constructs a multi-entity temporal hypergraph representing log attribute-value pair as nodes and connecting them with hyperedges, capturing critical connections in the data. HG-InsightLog introduces a multi-step query personalization mechanism enhancing the Personalized PageRank algorithm to rank hyperedges based on query relevance and contextual centrality to priortize critical connections. Top ranked hyperedges are extracted and converted back into log formats preserving temporal order and reducing context. Experimental results across multiple datasets demonstrate its superiority over existing methods, enhancing factual, causal, and analytical reasoning. Our approach enables smaller LLMs like LLaMA-8B to perform effective log-based QA. Being model-agnostic and training-free, it scales with evolving open-source LLMs without relying on proprietary systems.