An extension of a recently proposed single domain formulation of conjugated conduction–convection heat transfer problems is presented, taking into account the axial diffusion effects at both the walls and fluid regions, which are often of relevance in microchannels flows. The single domain formulation simultaneously models the heat transfer phenomena at both the fluid stream and the channel walls, by making use of coefficients represented as space variable functions, with abrupt transitions occurring at the fluid-wall interface. The generalized integral transform technique (GITT) is then employed in the hybrid numerical–analytical solution of the resulting convection–diffusion problem with variable coefficients. With axial diffusion included in the formulation, a nonclassical eigenvalue problem may be preferred in the solution procedure, which is itself handled with the GITT. To allow for critical comparisons against the results obtained by means of this alternative solution path, we have also proposed a more direct solution involving a pseudotransient term, but with the aid of a classical Sturm-Liouville eigenvalue problem. The fully converged results confirm the adequacy of this single domain approach in handling conjugated heat transfer problems in microchannels, when axial diffusion effects must be accounted for.