In order to design an environmentally friendly gold furnace that considers both traditional cultural elements and modern decorative elements, this paper puts forward the application of factor analysis in the image modeling design of an environmentally friendly gold furnace. Firstly, the elements of lines, colors, and patterns were extracted by factor analysis. By using the hierarchical structure model and factor analysis, the synchronous parameter fusion model of image modeling design factors of the environmental protection gold furnace is constructed to fuse the output reliability parameters of image modeling of the environmental protection gold furnace and adjust them adaptively. The factor analysis and process control of image modeling of environmental protection golden stoves are carried out using the method of differential feature analysis. Then, the Atlas and image Kanban are analyzed, and the image design factors of the environmental protection golden stove are excavated. Finally, the concepts of cultural space and cultural time are introduced. Based on the study of historical and material materials, the overall comparative analysis is carried out from three aspects: shape, color, and pattern. Combined with the extracted target image and the excavated design factors, the image modeling design of the environmental protection gold furnace is effectively carried out, providing design methods and sample references for the innovative design of the environmental protection gold furnace. The experimental results show that the mining design factors can effectively analyze the problems existing in the modeling design of the current environmental protection gold furnace, with a low bit error rate and strong practicability.