In view of the lack of spatial depth information in two-dimensional heat maps and the problems of complex calibration, high equipment cost, and limited use conditions in the existing multi-sensor schemes to establish the spatial temperature field model of the target object, this study proposes a spatial temperature field reconstruction scheme under a single thermal camera based on geometric constraints. Firstly, the temperature matrix collected by the thermal imager is remapped to the gray color space through the automatic threshold method, and the clear edge information of the target is obtained to filter out the irrelevant background. Then, the pose relationship of the target in the coordinate system of the thermal imager is directly calculated by the geometric constraints existing in the imaging process of the thermal imager and the imaging principle of the camera. Then, the 3D model of the target object is projected to the 2D heat map plane, and the texture mapping parameters of the 3D model are obtained. With the multi-view data acquisition of the target object by the thermal camera, the spatial temperature field reconstruction of the target object surface is completed. The experimental results show that, compared with the multi-sensor spatial temperature field reconstruction scheme, the average error of the single thermal imager scheme in this paper is only 4.3%, which can accurately and stably complete the spatial temperature field reconstruction of the target.