Using low temperature magnetoresistance measurements, the possibility to selectively move a domain wall locally by applying current pulses through a Au nanowire adjacent to a permalloy element is studied. We find that the domain wall depinning field is drastically modified with increasing current density due to the Joule heating and the Oersted field of the current, and controlled motion due to the Oersted field without any externally applied fields is achieved. By placing the domain wall at various distances from the Au wire, we determine the range of the Joule heating and the Oersted field and both effects can be separated.