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.
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