For turbulent flows in ducts axial heat conduction effects within the fluid can be important for low Prandtl number fluids (liquid metals). The paper presents an entirely analytical solution to the extended turbulent Graetz problem with Dirichlet wall boundary conditions. The solution is based on a selfadjoint formalism resulting from a decomposition of the convective diffusion equation for turbulent flow into a pair of first-order partial differential equations. The present approach, which is based on the solution method of Papoutsakis et al. for laminar pipe flow, is not plagued by any uncertainties arising from expansions in terms of eigenfunctions belonging to a nonselfadjoint operator. The obtained analytical results are compared with measurements of Gilliland et al. and Sleicher et al. showing good agreement between measured and predicted values.