Video reasoning requires models to identify and verify temporally localized evidence within long video sequences. Recent Video Large Language Models (Video-LLMs) have shown promising reasoning abilities when aligned with reinforcement learning, yet existing approaches typically rely on outcome-based rewards that supervise only the final prediction. Such supervision provides limited guidance on how models should discover the relevant temporal evidence during intermediate reasoning. In this work, we propose TimeThink, a reinforcement learning framework that explicitly guides temporal evidence discovery in Video-LLMs. Our key idea is to treat temporal clue steps as the fundamental optimization primitive of video reasoning, where each reasoning step references a candidate time interval in the video. We introduce a step-wise temporal process reward that provides localized credit assignment for these clues and a joint process--outcome optimization objective that balances reasoning fidelity with task correctness. To enable scalable training, we construct TimeThink-RFT-20K, a dataset with automatically derived temporal evidence segments. Extensive experiments across video reasoning, temporal grounding, and general video understanding benchmarks show that TimeThink consistently improves both temporal localization and reasoning performance, achieving state-of-the-art results among open-source video RL models.