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We study numerically thermal effects at the depinning transition of anelastic string driven in a two-dimensional uncorrelated disorder potential. Thevelocity of the string exactly at the sample critical force is shown to behaveas $V \sim T^\psi$, with $\psi$ the thermal rounding exponent. We show that thecomputed value of the thermal rounding exponent, $\psi = 0.15$, is robust andaccounts for the different scaling properties of several observables both inthe steady-state and in the transient relaxation to the steady-state. Inparticular, we show the compatibility of the thermal rounding exponent with thescaling properties of the steady-state structure factor, the universalshort-time dynamics of the transient velocity at the sample critical force, andthe velocity scaling function describing the joint dependence of thesteady-state velocity on the external drive and temperature.

Thermal rounding exponent of the depinning transition of an elastic string in a random medium