  We study the `string star' saddle, also known as the Horowitz-Polchinski
solution, in the middle of d+1 dimensional thermal AdS space. We show that
there's a regime of temperatures in which the saddle is very similar to the
flat space solution found by Horowitz and Polchinski. This saddle is
hypothetically connected at lower temperatures to the small AdS black hole
saddle. We also study, numerically and analytically, how the solutions are
changed due to the AdS geometry for higher temperatures. Specifically, we
describe how the solution joins with the thermal gas phase, and find the
leading correction to the Hagedorn temperature due to the AdS curvature.
Finally, we study the thermodynamic instabilities of the solution and argue for
a Gregory-Laflamme-like instability whenever extra dimensions are present at
the AdS curvature scale.
