We describe the temperature-dependence polarization properties of grating-gated AlGaN/GaN heterostructures at terahertz frequencies. Using the finite-difference time-domain method, it was demonstrated that as the temperature increases, the resonant frequency of the incident light was red-shifted. Simultaneously, a shorter gate length leads to a higher resonant frequency. In addition, at a lower temperature, the coupling efficiency of terahertz radiation and plasmon is higher. In our simulation results, the maximum modulation depth is 88%; at a gate length of 800 nm and lattice temperature of 77 K. For the same gate length, with higher electron gas concentrations and filling factor, greater modulation depths were produced. Studies on these properties may help in the design and optimization of terahertz detectors and modulators.