  The thermal rounding of the depinning transition of an elastic interface
sliding on a washboard potential is studied through analytic arguments and very
accurate numerical simulations. We confirm the standard view that well below
the depinning threshold the average velocity can be calculated considering
thermally activated nucleation of forward moving defects. However, we find that
the straightforward extension of this analysis to near or above the depinning
threshold does not fully describe the physics of the thermally assisted motion.
In particular, we find that exactly at the depinning point the average velocity
does not follow a pure power-law of the temperature as naively expected by the
analogy with standard phase transitions but presents subtle logarithmic
corrections. We explain the physical mechanisms behind these corrections and
argue that they are non-peculiar collective effects which may also apply to the
case of interfaces sliding on uncorrelated disordered landscapes.
