In flexible manufacturing systems, fast feedback from simulation solutions is required for effective tool path planning and parameter optimization. In the particular sub-domain of laser heating/cutting of thin rectangular plates, current state-of-the-art methods include frequency-domain (spectral) analytic solutions that greatly reduce the required computational time in comparison to industry standard finite element based approaches. However, these spectral solutions have not been presented previously in terms of Fourier methods and Fast Fourier Transform (FFT) implementations. This manuscript presents four different schemes that translate the problem of laser heating of rectangular plates into equivalent FFT problems. The presented schemes make use of the FFT algorithm to reduce the computational time complexity of the problem from O ( M 2 N 2 ) to O ( M N log ( M N ) ) (with M × N being the discretization size of the plate). The test results show that the implemented schemes outperform previous non-FFT approaches both in CPU and GPU hardware, resulting in 100 × faster runs. Future work addresses thermal/stress analysis, non-rectangular geometries and non-linear interactions (such as material melting/ablation, convection and radiation heat transfer).