The steady melting of several amorphous and semicrystalline polymers during spin welding is analyzed by solving a simplified set of momentum and energy balance equations, assuming a shear-rate and temperature-dependent viscosity. A numerical model is developed for predicting the flow field and the temperature distribution in the molten film. It is shown that the steady melting rate of the thermoplastic solid is affected by the variable viscosity, by the pressure applied on the parts to be joined, and by a balance between the viscous heat generation in the melt and the convection of colder material into the molten film. The convection of heat in the outflow direction is shown to have a much smaller effect on the melting process.