The reduced second-order approximation of the self-consistent phonon theory was applied some years ago for cubic metallic crystals whose interatomic interactions were approximated by the Morse and Lennard-Jones pair potential functions. Unfortunately, the parameters of these potentials were generally obtained with the help of semi-classical method basing on the classical static relationships between ground-state properties of a crystal and its interatomic potential, and the zero-point vibrations were taken into account only by certain corrections to the experimental data. Moreover, the further self-consistent calculations were being carried out semi-analytically which required some simplifications. In this paper we can reject them because all essential calculations are being carried out numerically. In the studies at high-temperature properties of selected fcc metallic crystals (Cu, Ag, Au) we take as a model of interatomic interactions the (alpha,m) Buckingham, (n,m) Lennard-Jones and (alpha,beta) Morse pair potentials with the parameters determined self-consistently with the help of the experimental data for the zero-point lattice constant, cohesive energy and isothermal compressibility. Our new theoretical results for pressure variations of the limiting temperatures of dynamical and thermodynamical stability and for the stability criteria are collected and compared with available experimental data.