In this paper it is investigated the influence of thermal oscillations of the crystal lattice on the formation of thermo-physical properties of transuranium metals. In the self-consistent thermodynamic model develops iterative scheme for calculating the thermodynamic characteristics, based on the method of successive approximations. The obtained values of the bulk modulus, heat capacity, linear coefficients of thermal expansion are in a good correlation with the experimental data at temperature T = 300 K. On the basis of a self-consistent analysis of the thermodynamic properties of the crystal lattice transuranium metals and alloys it is found that the Gruneisen parameters, which characterize the anharmonicity effects on the properties under consideration. It was found that at room temperatures the maximum lattice anharmonicity shows α-plutonium. Increase in the coefficient of thermal expansion for neptunium is also associated with anharmonicity. According to our estimates of temperature dependent thermodynamic parameters, americium is characterized by a relatively weak (compared with neptunium and plutonium) lattice anharmonicity, which is consistent with the observed phonon anharmonicity contribution to the heat capacity and confirmed by its relatively low value of the lattice Gruneisen parameter. The same conclusion is also made for curium.