  We study the effect of a transport current on the vortex-line lattice in
isotropic type-II superconductors in the presence of strong thermal
fluctuations by means of 'driven-diffusion' Monte Carlo simulations of a
discretized London theory with finite magnetic penetration depth. We calculate
the current-voltage (I-V) characteristics for various temperatures, for
transverse as well as longitudinal currents I. From these characteristics, we
estimate the linear resistivities R_xx=R_yy and R_zz and compare these with
equilibrium results for the vortex-lattice structure factor and the helicity
moduli. From this comparison a consistent picture arises, in which the melting
of the flux-line lattice occurs in two stages for the system size considered.
In the first stage of the melting, at a temperature T_m, the structure factor
drops to zero and R_xx becomes finite. For a higher temperature T_z, the second
stage takes place, in which the longitudinal superconducting coherence is lost,
and R_zz becomes finite as well. We compare our results with related recent
numerical work and experiments on cuprate superconductors.
