  The theory of current transport in a narrow superconducting channel
accounting for thermal fluctuations is revisited. The value of voltage
appearing in the sample is found as the function of temperature (close to
transition temperature $T-T_{\mathrm{c}}$ $\ll T_{\mathrm{c}}$) and bias
current $J<J_{\mathrm{c}}$ ( $J_{\mathrm{c}}$ is a value of critical current
calculated in the framework of the BCS approximation, neglecting thermal
fluctuations). It is shown that the careful analysis of vortex crossing of the
stripe results in considerable increase of the activation energy.
