  Thermally activated domain-wall (DW) motion driven by magnetic field and
electric current is investigated experimentally in out-of-plane magnetized
Pt(Co/Pt)$_3$ multilayers. We directly extract the thermal activation energy
barrier for DW motion and observe the dynamic regimes of creep, depinning, and
viscous flow. Further analysis reveals that the activation energy must be
corrected with a factor dependent on the Curie temperature, and we derive a
generalized Arrhenius-like equation governing thermally activated motion. By
using this generalized equation, we quantify the efficiency of current-induced
spin torque in assisting DW motion. Current produces no effect aside from Joule
heating in the multilayer with 7-\AA\ thick Co layers, whereas it generates a
finite spin torque on DWs in the multilayer with atomically thin 3-\AA\ Co
layers. These findings suggest that conventional spin-transfer torques from
in-plane spin-polarized current do not drive DWs in ultrathin Co/Pt
multilayers.
