Temperature gradient along superfluid He4 films in the presence of superflow

We have measured the nonlinear thermal conductance of a thin film of He4 as a function of temperature and heater power for a fixed film thickness. When heat transfer through the gas is included we obtain a qualitative understanding of the data in terms of Kosterlitz-Thouless theory as extended to finite superflow by Ambegaokar et al. The exponent in the power law relating conductance and heater power exhibits the universal jump at Tc predicted by its simple relationship to the areal superfluid density.