Turbulent natural convection in a horizontal fluid layer bounded by two infinite, isothermal, rigid plates is studied theoretically. The fluid layer is heated internally by uniformly distributed volumetric energy sources and externally by a constant rate of bottom heating. An approximate analysis of the Boussinesq equations of motion is performed to determine the behavior of the temperature field in various flow regions of the layer. By matching of the boundary layer and the turbulent core solutions, closed-form analytical expressions are obtained for the upper and the lower surface Nusselt numbers. The analytical results, which are valid over the entire range of turbulent thermal convection, compare favorably with all the existing experimental data.