The practical deployment of infrared imaging is hindered by its inherent output of low-resolution (LR) images. While the super-resolution (SR) technique is a promising remedy, we discover two major challenges concerning infrared image SR: preserving accurate thermal distributions, which are fundamental to infrared imaging, and addressing the ambiguity of high-frequency elements compared to visible images. To tackle these issues, we propose ThesIS, a tailored framework that utilizes Thermal-Physics guidance and dynamic high-frequency amplification for Infrared image Super-resolution to produce high-resolution (HR) images with accurate physical properties and delicate visual details. Specifically, Thermal Regularization is introduced to reconstruct the accurate thermal radiation distribution via the introduced Infrared Radiation Intensity Alignment Loss, mitigating the adverse effects of complex degradations while conducting initial upscaling. Additionally, we design a guidance mechanism to counter the randomness of the diffusion model, further refining the preservation of physical information. The proposed Dynamic High-Frequency Amplification effectively strengthens the ambiguous high-frequency information present in infrared images, leading to improved texture details and superior visual quality. Extensive experiments demonstrate that ThesIS successfully recovers accurate thermal information while delivering visually satisfying results with state-of-the-art performance. Furthermore, we introduce the InfraredSR dataset, which comprises 39,833 images at a resolution of 512 × 512, hoping to advance research in this field.