Heat transfer in the thermal entrance region of pipes is analyzed by the finite-difference method including the effect of axial fluid conduction. A hydrodynamically developed flow through a two-region pipe is investigated for constant surface temperatures by a step change and for insulated upstream and uniform wall heat flux in the downstream region. The rate of convergence is enhanced by discretizing the governing differential equation by an exact profile obtained from the analytical solution of the one-dimensional conduction-convection problem.