  The constant curvature (CC) black holes are higher dimensional
generalizations of BTZ black holes. It is known that these black holes have the
unusual topology of ${\cal M}_{D-1}\times S^1$, where $D$ is the spacetime
dimension and ${\cal M}_{D-1}$ stands for a conformal Minkowski spacetime in
$D-1$ dimensions. The unusual topology and time-dependence for the exterior of
these black holes cause some difficulties to derive their thermodynamic
quantities. In this work, by using globally embedding approach, we obtain the
Hawking temperature of the CC black holes. We find that the Hawking temperature
takes the same form when using both the static an global coordinates. Also it
is identical to the Gibbons-Hawking temperature of the boundary de Sitter
spaces of these CC black holes. Employing the same approach, we obtain the
Hawking temperature for the counterparts of CC black holes in de Sitter spaces.
