Silicon nitride (β-Si₃N₄) is a most promising thermal wave-transparent material. The accurate measurement of its high-temperature dielectric function is essential to solving the “black barrier” problem of hypersonic vehicles and accelerating the design of silicon nitride-based thermal wave-transparent materials. Direct experimental measurement at high temperature is a difficult job and the accuracy of classical molecular dynamics (CMD) simulations suffers the choice of empirical potential. In this work, we build a β-Si₃N₄ model on a nanoscale, train the deep learning potential (DLP) by using first-principles data, and apply the deep potential molecular dynamics (DPMD) to simulate the polarization relaxation process. The predicted energy and force by DLP are excellently consistent with first-principles calculations, which proves the high accuracy of DLP. The RMSEs for β-Si₃N₄ are quite low (0.00550 meV/atom for energy and 7.800 meV/Å for force). According to the Cole-Cole formula, the microwave dielectric function in the temperature range of 300–1000 K is calculated by using the deep learning molecular dynamics method. Compared with the empirical potential, the computational results of the DLP are consistent with the experimental results in the sense of order of magnitude. It is also found that the DPMD performs well in terms of computational speed. In addition, a mathematical model of the temperature dependence of the relaxation time is established to reveal the pattern of relaxation time varying with temperature. The high-temperature microwave dielectric function of silicon nitride is calculated by implementing large-scale and high-precision molecular dynamics simulations. It provides fundamental data for promoting the application of silicon nitride in high-temperature thermal transmission.