  We study the dynamics of a straight vortex line in a partially Bose-Einstein
condensed atomic gas. Using a variational approach to the stochastic field
equation that describes the dynamics of the condensate at nonzero temperature,
we derive the stochastic equations of motion for the position of the vortex
core. Using these results, we calculate the time it takes the vortex to spiral
out of the condensate. Due to the fact that we include thermal fluctuations in
our description, this lifetime of the vortex is finite even if its initial
position is in the center of the condensate.
