The heat transfer behaviour of a viscous fluid over a stretching/shrinking sheet driven by a uniform shear in the far field with a convective surface boundary condition is studied. The boundary layer equations governing the flow are reduced to ordinary differential equations using a similarity transformation. Using a numerical technique, these equations are then solved to obtain the temperature distributions and the heat transfer rate at the surface for various values of Prandtl number, stretching/shrinking parameter and convective parameter. Dual solutions are found to exist for the shrinking case, whereas for the stretching case, the solution is unique.