Slug flow forced convection in a circular duct is studied. The effect of viscous dissipation is analysed in the thermal entrance region. The temperature field and the local Nusselt number are determined analytically for any prescribed axial distribution of wall heat flux. Three examples are considered : a uniform wall heat Bur, a linearly varying wall heat flux and an exponentially varying wall heat flux. In the case of a uniform wall heat flux, it is shown that viscous dissipation reduces the value of the local Nusselt number in the whole duct. In the case of a linearly or exponentially increasing wall heat flux, viscous dissipation affects the local Nusselt number only in the thermal entrance region and becomes negligible in the fully developed region.