  We re-analyze the problem of thermally activated phase slips (TAPS) which can
dominate the behavior of sufficiently thin superconducting wires at
temperatures close to $T_C$. With the aid of an effective action approach we
evaluate the TAPS rate which turns out to exceed the rate found by D.E.
McCumber and B.I. Halperin, Phys. Rev. B {\bf 1}, 1054 (1970) within the TDGL
analysis by the factor $\sim (1-T/T_C)^{-1} \gg 1$. Additional differences in
the results of these two approaches arise at bias currents close to the
Ginzburg-Landau critical current where the TAPS rate becomes bigger. We also
derive a simple formula for the voltage noise across the superconducting wire
in terms of the TAPS rate. Our results can be verified in modern experiments
with superconducting nanowires.
