Abstract: The outlet fluid temperature (T_w2) and convective heat transfer coefficient (h) are two critical parameters for evaluating convective heat transfer characteristics in rock fractures. Conventional experimental methods are costly, and numerical simulations are computationally intensive and time-consuming, making them unsuitable for large-scale, rapid prediction. Moreover, some existing published h-formulas may produce anomalies such as negative values or numerical oscillations during calculation, indicating a lack of robustness. Therefore, this study aims to: (1) propose a more robust h-formula, (2) develop an efficient machine learning surrogate model for high-accuracy and rapid prediction of T_w2 and h, and (3) compare the effects of key controlling parameters. To address the robustness issue of the h-formula, this study first derived a new theoretical expression for h and validated its reliability by comparing it with existing formulas. Subsequently, to construct an efficient predictive model, four ensemble learning algorithms with different integration strategies were employed to model T_w2 and h separately, and their performance was evaluated and compared using six metrics, including RMSE and MAE. Additionally, feature importance analysis was conducted to quantify the influence of different parameters on T_w2 and h. The results demonstrate that the proposed h-formula presents stable computation without anomalies such as negative values or numerical oscillations, outperforming existing formulas. In terms of predictive performance, the XGB and SVR algorithms achieve the highest accuracy for T_w2 and h, respectively, with R values exceeding 0.95. Sensitivity analysis reveals that the ambient temperature (T_o) is the dominant factor influencing T_w2, while flow velocity (u), fracture aperture ( \delta ), and ambient temperature (T_o) collectively govern the variation in h. The proposed h-formula effectively overcomes the limitations of some existing formulas, providing a reliable tool for convective heat transfer calculations. Meanwhile, the developed machine learning models enable rapid batch prediction of T_w2 and h with high accuracy, significantly improving computational efficiency. These findings offer valuable insights for both theoretical research and engineering applications in geothermal energy extraction and hydrocarbon reservoir development.