The method of cluster dynamics (CD) is used to simulate the effect of the change in temperature of reactor pressure vessel on the time evolution of point defect clusters and the induced neutron embrittlement of $\alpha$-iron in a research nuclear reactor BR-2 (Mol, Belgium). For the two temperature regimes, the irradiation times, which provides the qualitatively change of the mean size and number density of self-interstitial atom clusters (SIAC) and vacancy clusters (VC), are found. Temperature is chosen of 573 K during all irradiation time at the first regime. Temperature is grown from the room one (288 K) to the value of 573 K during the start of nuclear reactor operation mode with time length about 381 hours; thereafter it does not change during next $\cong$ 14 days; then, at the second regime, the temperature decrease to the value of about 373 K. The neutron irradiation conditions are considered as the same for both temperature regimes, i.e. the neutron flux is of 1.39$\cdot10^{-7}$ dpa/s (E > 1 MeV) during 15 days. Master equation of CD is written as the system of stiff ordinary differential equations. The special numerical algorithm are applied in order avoid the problem of unstable solution. For this aim, the integration of master equation is carried out by the corresponding Code Linear Solver of Ordinary Differential Equations (LSODE) created in Livermore Lab (USA) in 1984. The transmission electron microscopy (TEM) and positron annihilation spectroscopy (PAS) experimental data are used for the calibration of CD model. The values of irradiation doses, which provide transition from the nucleation stage to the growth stage, are found for SIAC and VC on the assumption of both the constant temperature and the real change of the reactor pressure vessel temperature in the nuclear reactor BR-2. Based on the values of mean size and number density of SIAC and VC, the irradiation induced increasing of yield stress is estimated for both considered temperature regimes.