  We use holography in order to study the entropy of thermal CFTs on
(1+1)-dimensional curved backgrounds that contain horizons. Starting from the
metric of the BTZ black hole, we perform explicit coordinate transformations
that set the boundary metric in de Sitter or black-hole form. For a de Sitter
boundary, the dual picture describes a CFT at a temperature different from that
of the cosmological horizon. We determine minimal surfaces that allow us to
compute the entanglement entropy of a boundary region, as well as the
temperature affecting the energy associated with a probe quark on the boundary.
For an entangling surface that coincides with the horizon, we study the
relation between entanglement and gravitational entropy through an appropriate
definition of the effective Newton's constant. We find that the leading
contribution to the entropy is proportional to the horizon area, with a
coefficient that accounts for the degrees of freedom of a CFT thermalized above
the horizon temperature. We demonstrate the universality of our findings by
considering the most general metric in a (2+1)-dimensional AdS bulk containing
a non-rotating black hole and a static boundary with horizons.
