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Autonomous navigation in GPS-denied and visually degraded environments remains challenging for unmanned aerial vehicles (UAVs). To this end, we investigate the use of a monocular thermal camera as a standalone sensor on a UAV platform for real-time depth estimation and simultaneous localization and mapping (SLAM). To extract depth information from thermal images, we propose a novel pipeline employing a lightweight supervised network with recurrent blocks (RBs) integrated to capture temporal dependencies, enabling more robust predictions. The network combines lightweight convolutional backbones with a thermal refinement network (T-RefNet) to refine raw thermal inputs and enhance feature visibility. The refined thermal images and predicted depth maps are integrated into ORB-SLAM3, enabling thermal-only localization. Unlike previous methods, the network is trained on a custom non-radiometric dataset, obviating the need for high-cost radiometric thermal cameras. Experimental results on datasets and UAV flights demonstrate competitive depth accuracy and robust SLAM performance under low-light conditions. On the radiometric VIVID++ (indoor-dark) dataset, our method achieves an absolute relative error of approximately 0.06, compared to baselines exceeding 0.11. In our non-radiometric indoor set, baseline errors remain above 0.24, whereas our approach remains below 0.10. Thermal-only ORB-SLAM3 maintains a mean trajectory error under 0.4 m.