A line arrangement comprising an electrical line which has at least one electrical insulator and at least one electrical conductor which runs at least in some sections adjacently to the electrical insulator along a longitudinal axis of the electrical line. The line arrangement additionally has a passive heat dissipator which runs at least in some sections along the longitudinal axis and which has at least one heat-absorbing surface portion and at least one heat-emitting surface portion thermally connected to the heat-absorbing surface portion. The heat-absorbing surface portion is brought towards the electrical conductor at least to such an extent that the heat-absorbing surface portion forms a thermally operative connection to the electrical conductor in order to dissipate waste heat from the electrical conductor to the heat-emitting surface portion.