  We show that the temperature and entropy of a BTZ black hole are invariant
under T-duality to next to leading order in $M_\star^{-2}$, $M_\star$ being the
scale suppressing higher-curvature/derivative terms in the Lagrangian. We work
in the framework of a two-parameter family of theories exhibiting T-duality,
which includes (but goes beyond) String Theory. Interestingly enough, the
AdS/CFT correspondence enforces quantization conditions on these parameters. In
the particular case of bosonic/heterotic string theory, our results extend
those of a classical paper by Horowitz and Welch. For generic (albeit
quantized) values of the parameters, it suggests that T-duality might be an
interesting tool to constrain consistent low-energy effective actions while
entailing physical equivalences outside String Theory. Moreover, it generates a
new family of regular asymptotically flat black string solutions in
three-dimensions.
