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In this paper, we introduce SC-Lane, a novel slope-aware and temporally consistent heightmap estimation framework for 3D lane detection. Unlike previous approaches that rely on fixed slope anchors, SC-Lane adaptively determines the fusion of slope-specific height features, improving robustness to diverse road geometries. To achieve this, we propose a Slope-Aware Adaptive Feature module that dynamically predicts the appropriate weights from image cues for integrating multi-slope representations into a unified heightmap. Additionally, a Height Consistency Module enforces temporal coherence, ensuring stable and accurate height estimation across consecutive frames, which is crucial for real-world driving scenarios. To evaluate the effectiveness of SC-Lane, we employ three standardized metrics-Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and threshold-based accuracy-which, although common in surface and depth estimation, have been underutilized for road height assessment. Using the LiDAR-derived heightmap dataset introduced in prior work, we benchmark our method under these metrics, thereby establishing a rigorous standard for future comparisons. Extensive experiments on the OpenLane benchmark demonstrate that SC-Lane significantly improves both height estimation and 3D lane detection, achieving state-of-the-art performance with an F-score of 64.3%, outperforming existing methods by a notable margin. For detailed results and a demonstration video, please refer to our project page: https://parkchaesong.github.io/sclane/