  We present a new approach to the calculation of thermodynamic functions for
crossing-invariant models solvable by Bethe Ansatz. In the case of the XXZ
Heisemberg chain we derive, for arbitrary values of the anysotropy, a {\bf
single} non--linear integral equation from which the free energy can be exactly
calculated. The high--temperature expansion follows in a sistematic and
relatively simple way. For low temperatures we obtain the correct central
charge and predict the analytic structure of the full expansion around $T=0$.
Furthermore, we derive a single non-linear integral equation describing the
finite--size ground--state energy of the Sine--Gordon quantum field theory.
PACS: 05.30, 03.70. 75.10.5
