  We present a unified approach to the Thermodynamic Bethe Ansatz (TBA) for
magnetic chains and field theories that includes the finite size (and zero
temperature) calculations for lattice BA models. In all cases, the free energy
follows by quadratures from the solution of a {\bf single} non-linear integral
equation (NLIE). [A system of NLIE appears for nested BA]. We derive the NLIE
for: a) the six-vertex model with twisted boundary conditions; b) the XXZ chain
in an external magnetic field $h_z$ and c) the sine-Gordon-massive Thirring
model (sG-mT) in a periodic box of size $\b \equiv 1/T $ using the light-cone
approach. This NLIE is solved by iteration in one regime (high $T$ in the XXZ
chain and low $T$ in the sG-mT model). In the opposite (conformal) regime, the
leading behaviors are obtained in closed form. Higher corrections can be
derived from the Riemann-Hilbert form of the NLIE that we present.
