  Thermal fluctuations of the Josephson current $I$ induced by the magnetic
flux through a ring of $N$ superconducting grains are studied. When a
half-fluxon is threading the ring, $I$ exhibits incoherent transitions between
the two degenerate states due to thermal phase slips. We propose a new
numerical method to deal with both equilibrium and dynamic properties of
Josephson systems. Computed transition rate has the form $\Gamma =
A(N)\exp[-B(N)/T]$, where $B(N)$ agrees with the analytical result derived for
the energy barrier associated with phase slips. In the non-degenerate case
(e.g., at a quarter-fluxon) the equilibrium value of $I$ decreases with $T$ due
to harmonic excitations and then gets destroyed by phase slips.
