Based on the electromagnetic fluid model, the effects of electron temperature and plasma density on the nonlinear frequency shift of electron acoustic wave in a relativistic hot plasma are investigated. The nonlinear frequency shift equation of electron acoustic wave is obtained by using the nonlinear frequency shift theory and perturbation method. The results show that the plasma density, the first harmonic amplitude and the electron temperature are the main factors that determine the nonlinear frequency shift of electron acoustic wave in relativistic hot plasma. For weak excitation, the nonlinear frequency shift increases with the increase of electron temperature and the first harmonic amplitude, and the plasma density inhibits the nonlinear frequency shift. The impact of electron temperature and the plasma density on nonlinear frequency shift shows a strong nonlinear character. The results provide a theoretical evidence for understanding the high power laser-plasma interaction and the generation of harmonics.