Stationary forced convection in a rectangular duct is investigated in the case of slug flow by taking into account the effect of viscous dissipation. Axially-varying heat fluxes are prescribed on the four duct walls. Under the assumption that the axial heat conduction in the fluid is negligible, an analytical solution for the thermal entrance region is obtained by employing a superposition method. More precisely, the superposition method allows one to reduce the three-dimensional boundary value problem to a two-dimensional problem which is solved by the Laplace transform technique. The dimensionless temperature and the axially local Nusselt number are determined. Special attention is devoted to the eight fundamental boundary conditions of axially uniform wall heat fluxes and to the case of a peripherally uniform wall heat flux which undergoes an exponential axial variation.