Three-dimensional (3D) thermography technology combines the advantages of 3D reconstruction and infrared thermal imaging, enabling simultaneously acquisition of both the temperature distribution and geometric structure information of an object’s surface. It is an effective method to visually present the surface information of industrial materials. However, in the single view imaging environment with dust interference, the conventional 3D thermography method is difficult to apply. Therefore, this paper develops a 3D thermal imaging system using an infrared thermal camera and a depth camera, and proposes a single-view 3D thermal imaging method for the surface of industrial materials under dust interference. Firstly, this paper establishes a joint external parameter calibration model based on virtual imaging to solve the challenge of spatial synchronization in single-view imaging devices. Secondly, based on the principle of radiation temperature measurement, an approximate compensation method for infrared temperature measurement is proposed to obtain the temperature distribution with small error under dust interference. Then, to solve the problem of depth information loss and view occlusion in single-view 3D thermography, a single-view 3D thermal imaging method based on depth map rendering and viewpoint optimization is proposed to achieve fusion of temperature and topography data of the measured object under the optimal view. Experimental results show that the proposed method can effectively realize single-view 3D thermography of the surface of objects under dust interference, retain more temperature and depth information, and reduce infrared temperature measurement errors