We study the creep motion of an elastic string in a two dimensional pinning landscape by Langevin dynamics simulations. We find that the Velocity-Force characteristics are well described by the creep formula predicted from phenomenological scaling arguments. We analyze the creep exponent μ, and the roughness exponent ζ. Two regimes are identified: when the temperature is larger than the strength of the disorder we find μ≈1/4 and ζ≈2/3, in agreement with the quasi-equilibrium-nucleation picture of creep motion; on the contrary, lowering enough the temperature, the values of μ and ζ increase showing a strong violation of the latter picture.