Temperature gradient along superfluidHe4films in the presence of superflow

We have measured the nonlinear thermal conductance of a thin film of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ 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 $T_c$ predicted by its simple relationship to the areal superfluid density.