  Asymptotically exact low temperature expansions for the $s=1/2$ Heisenberg
XXZ chains with boundaries are implemented by using the boundary conformal
field theory. It is found that for $1/2<\Delta\leq 1$, ($\Delta$, an
anisotropic parameter) the boundary terms of the spin susceptibility and the
specific heat coefficient show divergent behaviors, as temperature decreases.
The degrees of the divergence coincide with those obtained by the Bethe ansatz
method at zero temperature. Such low-temperature anomalous behaviors at
boundaries are deeply related with finite-temperature corrections of the
boundary entropy or the ground state degeneracy, the presence of which yields a
very sensitive response of spin excitations.
