While large vision-language models (VLMs) show promise for object goal navigation, current methods still struggle with low success rates and inefficient localization of unseen objects--failures primarily attributed to weak temporal-spatial reasoning. Meanwhile, recent attempts to inject reasoning into VLM-based agents improve success rates but incur substantial computational overhead. To address both the ineffectiveness and inefficiency of existing approaches, we introduce Hydra-Nav, a unified VLM architecture that adaptively switches between a deliberative slow system for analyzing exploration history and formulating high-level plans, and a reactive fast system for efficient execution. We train Hydra-Nav through a three-stage curriculum: (i) spatial-action alignment to strengthen trajectory planning, (ii) memory-reasoning integration to enhance temporal-spatial reasoning over long-horizon exploration, and (iii) iterative rejection fine-tuning to enable selective reasoning at critical decision points. Extensive experiments demonstrate that Hydra-Nav achieves state-of-the-art performance on the HM3D, MP3D, and OVON benchmarks, outperforming the second-best methods by 11.1%, 17.4%, and 21.2%, respectively. Furthermore, we introduce SOT (Success weighted by Operation Time), a new metric to measure search efficiency across VLMs with varying reasoning intensity. Results show that adaptive reasoning significantly enhances search efficiency over fixed-frequency baselines.