Thermal imaging can greatly enhance the application of intelligent unmanned aerial vehicles (UAV) in challenging environments. However, the inherent low resolution of thermal sensors leads to insufficient details and blurred boundaries. Super-resolution (SR) offers a promising solution to address this issue, while most existing SR methods are designed for fixed-scale SR. They are computationally expensive and inflexible in practical applications. To address above issues, this work proposes a novel any-scale thermal SR method (AnyTSR) for UAV within a single model. Specifically, a new image encoder is proposed to explicitly assign specific feature code to enable more accurate and flexible representation. Additionally, by effectively embedding coordinate offset information into the local feature ensemble, an innovative any-scale upsampler is proposed to better understand spatial relationships and reduce artifacts. Moreover, a novel dataset (UAV-TSR), covering both land and water scenes, is constructed for thermal SR tasks. Experimental results demonstrate that the proposed method consistently outperforms state-of-the-art methods across all scaling factors as well as generates more accurate and detailed high-resolution images. The code is located at https://github.com/vision4robotics/AnyTSR.