On general grounds, high-derivative gravities are known to be in conflict with causality and unitarity. Perturbative string theory is free from these issues. In order to further understand what specific stringy ingredient plays a key role in this problem, we explore the behavior under T-duality of the temperature and black hole entropy in a two-parameter family of quadratic gravity theories, which includes (but goes beyond) String Theory. We focus on the three-dimensional case. T-duality generates a new family of regular asymptotically flat black string solutions, while leaving the temperature and entropy invariant. In the particular case of bosonic/heterotic string theory, our results extend those of a classical paper by Horowitz and Welch. Interestingly, the AdS/CFT correspondence enforces quantization conditions on the otherwise unrestricted parameters.