  It might be tempting to consider that the two-dimensional anti-de Sitter
black hole in the Jackiw-Teitelboim model is thermally hot by invoking the
non-vanishing surface gravity. So, one might expect that the local temperature
would also be blue-shifted near the horizon, while it would vanish at infinity
because of the Tolman factor of the local temperature. In this paper, we will
show that the local temperature vanishes everywhere, which respects the
equivalence principle perfectly in contrast to the case of the asymptotically
flat black holes recovering the equivalence principle just at the horizon. In
other words, the origin of radiation for a fixed observer comes from the Unruh
effect rather than the Hawking effect. If the inward and outward fluxes are
defined non-trivially at the horizon, then the local temperature of the black
hole takes the usual Tolman form; however, the divergent Tolman temperature at
the horizon is incompatible with the finite local energy density there.
