  A semi-phenomenological model is proposed to study dynamics and stedy states
of magnetic fluxes and currents in mesoscopic rings and cylinders at non-zero
temperature. The model is based on a Langevin equation for flux subject to
zero-mean thermal equilibrium Nyquist noise. Quenched randomness, which mimics
disorder, is included via the fluctuating parameter method. In the noiseless
case, the stability threshold (critical temperature) exists below which
selfsustaining currents can run even if the external flux is switched off. It
is shown that selfsustaining and persistent currents survive in presence of
Nyquist noise and quenched disorder but the stability threshold can be shifted
by noise.
