Infrared temperature measurement ubiquitously finds applications across multifarious domains. The surface infrared emissivity constitutes the critical parameter influencing the precision of infrared temperature measurement. Therefore, investigating the surface infrared emissivity is of tremendous significance. This paper establishes an infrared emissivity analytical model for rough texture surfaces by considering the repercussions of roughness on the infrared emissivity of material surfaces. First, power spectrum analysis of random roughness is performed. The positive and negative power law components of the rough surface model are constructed using the Monte Carlo method and fractal theory, respectively. Second, based on the perturbation method and Kirchhoff approximation, the infrared emissivity model for rough textured surfaces is established. Third, the infrared emissivity of rough textured surfaces with different fractal dimensions (D), characteristic length scales (G), and surface textures is simulated using the FDTD optical simulation software to validate the efficacy of the infrared emissivity model. Finally, the infrared emissivity model is applied to the temperature measurement system of aluminum alloy friction stir welding. The infrared measurement precision before and after rectification is contrasted and scrutinized to validate the accuracy of this model.