  We compute the decay rate of a metastable cosmic string in contact with a
thermal bath by finding the instanton solution. The new feature is that this
decay rate is found in the context of non thermal scalar fields in contact with
a thermal bath of photons. In general, to make topologically unstable strings
stable, one can couple them to such a bath. The resulting plasma effect creates
metastable configurations which can decay from the false vacuum to the true
vacuum. In our specific set-up, the instanton computation is realized for the
case of two out-of-equilibrium complex scalar fields : one is charged and
coupled to the photon field, and the other is neutral. New effects coming from
the thermal bath of photons make the radius of the nucleated bubble and most of
the relevant physical quantities temperature-dependent. However, the
temperature appears in a different way than in the purely thermal case, where
all scalar fields are in thermal equilibrium. As a result of the tunneling, the
core of the initial string melts while bubbles of true vacuum expand at the
speed of light.
