  We consider the low-temperature limit of the long-distance asymptotic
behavior of the finite temperature density-density correlation function in the
one-dimensional Bose gas derived recently in the algebraic Bethe ansatz
framework. Our results confirm the predictions based on the Luttinger liquid
and conformal field theory approaches. We also demonstrate that the amplitudes
arising in this asymptotic expansion at low-temperature coincide with the
amplitudes associated with the so-called critical form factors.
