  We calculate the two-particle local correlation for an interacting 1D Bose
gas at finite temperature and classify various physical regimes. We present the
exact numerical solution by using the Yang-Yang equations and Hellmann-Feynman
theorem and develop analytical approaches. Our results draw prospects for
identifying the regimes of coherent output of an atom laser, and of
finite-temperature ''fermionization'' through the measurement of the rates of
two-body inelastic processes, such as photo-association.
