Equivalence of TBA and QTM

The traditional thermodynamic Bethe ansatz equations for the XXZ model at \ Delta\ greater than or equal to 1 are derived within the quantum transfer m atrix method. This provides further evidence of the equivalence of both met hods. Most importantly, we derive an integral equation for the free energy formulated for just one unknown function. This integral equation differs in physical and mathematical aspects to the established ones. The single inte gral equation is analytically continued to the regime \Delta\ < 1.