A new set of relativistic mean-field theory (RMFT) parameters, NL4, ensuring a better description of the average nuclear energy as given by the new Lublin–Strasbourg mass formula, is used in a self-consistent description of 171 spherical even-even nuclei at temperatures 0≤T≤4 MeV. Single-particle level densities for this sample of nuclei are determined by analyzing the data obtained for various temperatures. The average dependence of the single-particle level density on mass number A and isospin is given and compared with previous estimates obtained using the RMFT-NL3, Thomas–Fermi and semiclassical Skyrme SkM* approaches.