Accurate estimation of the human circadian phase plays an important role in personalized health monitoring, but most existing wearable-based approaches operate retrospectively and require full circadian cycle recordings, leading to high estimation latency and substantial data and computational burden for real-time deployment on edge devices. In this study, we investigated whether circadian phase can be estimated in real time using only short historical windows of wearable data. We propose a low latency framework that estimates instantaneous circadian phase from past observations, with a cosinor-fitted core body temperature rhythm serving as the reference. Data from a free-living field study involving 14 participants were used to systematically evaluate the effects of sensor modality selection, historical window length, and model class under participant-based cross-validation. The results showed that estimation accuracy improves with increasing window length but saturates at approximately 8 hours of history. Tree-based models reached a performance plateau beyond 480 minutes, whereas sequence-based models continued to benefit from longer temporal contexts. When relying solely on light exposure and physical activity, the proposed approach achieved a mean circular mean absolute error (CMAE) of 1.19 h. These findings provide practical guidance for efficient and deployable real-time circadian phase monitoring using wearables.