  We examine a two parameter family of gravitational actions which contains
higher-derivative terms. These are such that the entire action is invariant
under corrected T-duality rules, which we derive explicitly. Generically this
action does not describe low energy string backgrounds except for isolated
choices for the parameters. Nevertheless, we demonstrate that in this theory
the entropy and the temperature of generic black hole solutions are T-duality
invariant. This further supports the idea put forward in our previous work that
T-duality might provide physical equivalences beyond the realm of string
theory.
