  A generalized theory of open quantum systems combined with mean-field theory
is used to study a superconducting wire in contact with thermal baths at
different temperatures. It is shown that, depending on the temperature of the
colder bath, the temperature of the hotter bath can greatly exceed the
equilibrium critical temperature, and still the local temperature in the wire
is maintained below the critical temperature and hence the wire remains in the
superconducting state. The effects of contact areas and disorder are studied.
Finally, an experimental setup is suggested to test our predictions.
