  We investigate dilaton-gravity models whose solutions contain a large portion
of the static patch of dS$_2$. The thermodynamic properties of these theories
are considered both in the presence of a finite Dirichlet wall, as well as for
asymptotically near-AdS$_2$ boundaries. We show that under certain
circumstances such geometries, including those endowed with an asymptotically
near-AdS$_2$ boundary, can be locally and even globally thermodynamically
stable within particular temperature regimes. First order phase transitions
reminiscent of the Hawking-Page transition are discussed. For judiciously
chosen models, the near-AdS$_2$ boundary can be viewed as a completion of the
stretched cosmological dS$_2$ horizon. We speculate on candidate microphysical
models.
