We present a new method based on fast Fourier transform (FFT) for evaluating the thermal expansion coefficient and thermomechanical properties of thin films. The silicon nitride thin films deposited on Corning glass and Si wafers were prepared by plasma-enhanced chemical vapor deposition in this study. The anisotropic residual stress and thermomechanical properties of silicon nitride thin films were studied. Residual stresses in thin films were measured by a modified Michelson interferometer associated with the FFT method under different heating temperatures. We found that the average residual-stress value increases when the temperature increases from room temperature to 100°C. Increased substrate temperature causes the residual stress in ${\mathrm{SiN}}_x$ film deposited on Si wafers to be more compressive, but the residual stress in ${\mathrm{SiN}}_x$ film on Corning glass becomes more tensile. The residual-stress versus substrate-temperature relation is a linear correlation after heating. A double substrate technique is used to determine the thermal expansion coefficients of the thin films. The experimental results show that the thermal expansion coefficient of the silicon nitride thin films is $3.27\times {10}^{-6}°{\mathrm{C}}^{-1}$. The biaxial modulus is 1125 GPa for ${\mathrm{SiN}}_x$ film.