The relaxation of temperature, coupling parameters, the excess part of equation of state, and the correlation energy of the non-isothermal hot dense plasmas are considered on the basis of the method of effective interaction potentials. The electroneion effective interaction potential for the hot dense plasma is discussed. The accuracy of description of the dense plasma properties by the effective electroneion interaction potential is demonstrated by the agreement of the derived quantities like stopping power and transport coefficients calculated using our methodology with the results of the finite-temperature Kohn-Sham density-functional theory molecular dynamics, and orbital-free molecular dynamics results as well as with the data obtained using other theoretical approaches.