In this paper, we have studied the PHASE TRANSITION of nucleons, between a paired PHASE and a Fermi gas state, in 89Y and 208Pb nuclei. In order to conduct this study, the nuclear level density parameters of 89Y and 208Pb nuclei in the constant temperature model were extracted by the using of experimental data from Oslo group. The extracted results were used in the calculation of the cross sections of 208Pb (n, el), 208Pb(p, el), 89Y(n, el) and 89Y(p, el) nuclear reactions. According to the good agreement between the extracted results and corresponding experimental values for the cross sections, a constant temperature behavior, which can be interpreted as an evidence for the pairing PHASE TRANSITION, is confirmed for the nuclei. In addition, heat capacity of 89Y and 208Pb nuclei has been extracted from the experimental level densities and the effect of pairing PHASE TRANSITION of nucleons is studied within this thermodynamic quantity.