In the present paper, we have been investigated deeply and parametrically the speed response of Si PIN photodiodes employed in high temperature-irradiated environment. The radiation-induced photodiodes defects can modify the initial doping concentrations, creating generation-recombination centres and introducing trapping of carriers. Additionally, rate of the lattice defects is thermally activated and reduces for increasing irradiation temperature as a result of annealing of the damage. Nonlinear relations are correlated to investigate the current-voltage and capacitance-voltage dependences of the Si PIN photodiodes, where thermal and gamma irradiation effects are considered over the practical ranges of interest. Both the ambient temperature and the irradiation dose possess sever effects on the electro-optical characteristics and consequently the photo-response time and SNR of Si PIN photodiodes. In this paper, we derive the transient response of a Si PIN photodiode for photogeneration currents, when it is exposed to gamma radiation at high temperature. An exact model is obtained, which may be used to optimize the responsivity and speed of these irradiated devices over wide range of the affecting parameters.