We employ the Landau-Lifshitz-Bloch (LLB) equation to investigate current-induced domain wall motion at finite temperatures by numerical micromagnetic simulations. We extend the LLB equation with spin torque terms that account for the effect of spin-polarized currents and we find that the velocities depend strongly on the interplay between adiabatic and non-adiabatic spin torque terms. As a function of temperature, we find non-monotonous behavior, which might be useful to determine the relative strengths of the spin torque terms experimentally.