In this paper, the thermo-fluid-dynamic field resulting from the coupling of laminar forced convection along and conduction inside a heated flat plate is studied by means of two expansions. The first one, describing the field in the leading edge region of the flat plate, is a regular series. The second expansion, which is asymptotic, includes eigensolutions. Moreover, by means of the Padé approximant technique, it is possible to extend the validity of the first expansion over its range of convergence and hence to obtain the description of the entire field.