  We report on a new approach to the calculation of thermodynamic functions for
crossing-invariant models solvable by Bethe Ansatz. In the case of the XXZ
Heisenberg chain we derive, for arbitrary values of the anysotropy, a single
non-linear integral equation from which the free energy can be exactly
calculated.These equations are shown to be equivalent to an infinite set of
algebraic equations of Bethe type which provide alternatively the
thermodinamics.
  The high-temperature expansion follows in a sistematic and relatively simple
way from our non-linear integral equations. 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.
