The influence of initial plasma temperature on the proton generation under Compton scattering is studied by using the model of multi-photon nonlinear Compton scattering and two-dimensional particle-in-cell (PIC) simulation, and the results are numerically simulated. The results show that the amounts of produced proton have an even noteworthy increase along with the increase of the initial plasma temperature than that before the Compton scattering, the energy spectrum curves of the protons before and after the target tend to be smooth, and the differences in the number of accelerated protons are decreased. When the incident laser intensity is increased, the relative extents of the proton number increasing are clearly decreased along with the increase of the initial plasma temperature. When the incident laser intensity is decreased, the energy spectrum curves of the protons still have clear differences with the increase of the initial plasma temperature, and the number and speed of protons are clearly increased.