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In this paper, we propose AnyTSR, a novel super-resolution (SR) method that solves the low-resolution problem of thermal imaging sensors to improve the utilization of thermal imaging technology for intelligent unmanned aerial vehicles (UAVs). To solve the high computational cost and inflexibility problems of existing fixed-scale SR methods, we develop AnyTSR, which performs arbitrary-scale thermal imaging SR within a single model. A novel image encoder is proposed to explicitly assign feature codes to enable accurate and flexible representations, and an innovative arbitrary-scale upsampler is proposed to effectively integrate coordinate offset information into local feature ensembles to better understand spatial relationships and reduce artifacts. In addition, a new dataset, UAV-TSR, which includes both land and water scenes is constructed. Experimental results show that AnyTSR outperforms state-of-the-art methods at all magnifications and generates more accurate and detailed high-resolution images. The source code is available at https://github.com/vision4robotics/AnyTSR .