The Nariai limit has no singularities, the cosmological and black hole horizons have the same area, and they can be mapped to each other by a discrete reflection symmetry in any causal patch.
In a semi-classical treatment, the de Sitter cosmological horizon can be thought of as absorbing or emitting depending on the point of view.
Similarly, for a black hole that has been around for a long time, the horizon can be thought of as emitting or absorbing depending on whether you take the point of view of infalling matter or outgoing Hawking radiation.
This was elaborated by Leonard Susskind into black hole complementarity, which states that any interior parts of a black hole solution, in either the past and future horizon interpretation, can be holographically related by a unitary change of basis to the quantum mechanical description of the horizon itself.
The Nariai solution is the limit of the largest black hole in a space that is de Sitter at large distances.
In the Nariai limit, the black hole and de Sitter horizon can be interchanged just by changing the sign of the coordinate
When there is additional matter density, the solution can be thought of as an Einstein spherical universe with two antipodal black holes.
The constant-time radius of the circle expands exponentially into the future and the past, and this is Nariai's original form.
This is a manifestation of Mach's principle in self-contained causal patches, if the cosmological horizon is included as "matter", like its symmetric counterpart, the black hole.
The quantity that is the temperature of the black hole is hard to define, because there is no asymptotically flat space to measure it relative to.