We present a description of the current-voltage characteristics of hot electron bolometers in terms of the current-dependent intrinsic resistive transition of NbN films. We find that, by including this current dependence, we can correctly predict the complete current-voltage characteristics, showing excellent agreement with measurements for both low and high bias and for small as well as large devices. It is assumed that the current dependence is due to vortex-antivortex unbinding as described in the Berezinskii–Kosterlitz–Thouless theory. The presented approach will be useful in guiding device optimization for noise and bandwidth.