Aircraft structures such as skins, frames, and beams are widely constructed using non-ferromagnetic metals, including aluminum alloys and titanium alloys. During the manufacturing and service processes, these structures are prone to surface defects. The identification and quantitative assessment of surface defects are of critical importance. Eddy current pulsed thermography (ECPT) achieves defect identification by utilizing eddy current heating combined with thermal imaging. It offers advantages such as portability, non-contact operation, and pollution-free detection. Traditional post-processing methods for thermal images primarily rely on identifying defects through high-temperature regions, but they face challenges in reconstructing the morphology of defects. In this paper, we propose a model-based approach for the reconstruction of profiles of surface defects. Specifically, the approach involves constructing an induced electromagnetic field model for the material under inspection, establishing a sensitivity map that correlates eddy currents with the conductivity, and employing the least squares optimization method to reconstruct the defect profile. Experimental evaluations involving various types of defects are conducted to validate the effectiveness of the proposed method.