  The free energy and correlation lengths of the spin-1/2 $XYZ$ chain are
studied at finite temperature. We use the quantum transfer matrix approach and
derive non-linear integral equations for all eigenvalues. Analytic results are
presented for the low-temperature asymptotics, in particular for the critical
$XXZ$ chain in an external magnetic field. These results are compared to
predictions by conformal field theory. The integral equations are solved
numerically for the non-critical $XXZ$ chain and the related spin-1 biquadratic
chain at arbitrary temperature.
