  We study stochastic behavior of a single vortex loop appeared in imperfect
Bose gas. Dynamics of Bose-condensate is supposed to obey Gross-Pitaevskii
equation with additional noise satisfying fluctuation-dissipation relation. The
corresponding Fokker-Planck equation for probability functional has a solution
$\mathcal{P}(\{{\psi}(\mathbf{r})\})=\mathcal{N}\exp (-H{\psi}(\mathbf{r)}
/T),$ where $H\psi(\mathbf{r})$ is a Ginzburg-Landau free energy. Considering a
vortex filaments as a topological defects of the field ${\psi}(\mathbf{r})$ we
derive a Langevin-type equation of motion of the line with correspondingly
transformed stirring force. The respective Fokker-Planck equation for
probability functional $\mathcal{P}(\{\mathbf{s}(\xi)\})$ in vortex loop
configuration space is shown to have a solution of the form
$\mathcal{P}(\{\mathbf{s}(\xi)\})=\mathcal{N}\exp (-H{\mathbf{s}} /T),$ where
$\mathcal{N}$ is a normalizing factor and $H{\mathbf{s}}$ is energy of vortex
line configurations. In other words a thermal equilibrium of Bose-condensate
results in a thermal equilibrium of vortex loops appeared in Bose-condensate.
Some consequences of that fact and possible violations are discussed.
