Temporal Knowledge Graph (TKG) forecasting faces significant challenges due to distribution shifts and poor inductive generalization in parametric models. While Large Language Models (LLMs) offer potent semantic reasoning, existing LLM-based approaches struggle with implicit modality alignment and suboptimal graph linearization, failing to capture complex topologies without retraining. To bridge this gap, we propose ExE-LLM, a training-free, test-time adaptive framework that reframes TKG prediction as explicit evidence-driven reasoning. Our core philosophy is to decouple topological calculation from semantic reasoning: a heuristic module translates latent graph signals into natural language evidence, enabling the LLM to perform multi-source judgment. ExE-LLM incorporates a task-aware scheduler for test-time adaptation, a heuristic synthesizer for explicit modality alignment, and a self-diagnosis module for iterative optimization. Extensive experiments on four benchmarks demonstrate that ExE-LLM achieves SOTA performance in inductive settings, significantly outperforming fully trained graph neural networks without updating LLM parameters. The source code is available at https://github.com/JENLISA4EVER/ExE-LLM.

Temporal Knowledge Graphs (TKGs) are vital for event prediction, yet current methods face limitations. Graph neural networks mainly depend on structural information, often overlooking semantic understanding and requiring high computational costs. Meanwhile, Large Language Models (LLMs) support zero-shot reasoning but lack sufficient capabilities to grasp the laws of historical event development. To tackle these challenges, we introduce a training-free Analogical Replay (AnRe) reasoning framework. Our approach retrieves similar events for queries through semantic-driven clustering and builds comprehensive historical contexts using a dual history extraction module that integrates long-term and short-term history. It then uses LLMs to generate analogical reasoning examples as contextual inputs, enabling the model to deeply understand historical patterns of similar events and improve its ability to predict unknown ones. Our experiments on four benchmarks show that AnRe significantly exceeds traditional training and existing LLM-based methods. Further ablation studies also confirm the effectiveness of the dual history extraction and analogical replay mechanisms.