  We analyze the depinning transition of a driven interface in the 3d
random-field Ising model (RFIM) with quenched disorder by means of Monte Carlo
simulations. The interface initially built into the system is perpendicular to
the [111]-direction of a simple cubic lattice. We introduce an algorithm which
is capable of simulating such an interface independent of the considered
dimension and time scale. This algorithm is applied to the 3d-RFIM to study
both the depinning transition and the influence of thermal fluctuations on this
transition. It turns out that in the RFIM characteristics of the depinning
transition depend crucially on the existence of overhangs. Our analysis yields
critical exponents of the interface velocity, the correlation length, and the
thermal rounding of the transition. We find numerical evidence for a scaling
relation for these exponents and the dimension d of the system.
