  In this paper, we present three analytic AdS black hole solutions in a
two-dimensional dilaton gravity theory, which contains two scalar fields
non-minimally coupled to gravity. Our solutions I and II contain two arbitrary
integration constants in the blackening factor $f(r)$, with which we can impose
an extremality condition. Solution I coincides with a previously reported AdS
black hole when one of the integration constants vanishes in $f(r)$ and we have
only one non-trivial scalar field. Solution III corresponds to an extreme black
hole configuration with an asymptotically finite constant dilaton field. For
all of our solutions, both non-extremal and extremal, the scalar curvature is
constant and negative, corresponding to $AdS_2$ spacetime. Thus, we show that
pure $AdS_2$ geometry arises outside the event horizon of all our black hole
configurations, not only in the near horizon region. In order to elucidate
their black hole nature, we explore the causal structure of solutions I and II
with the aid of suitable Kruskal-like coordinates and Penrose diagrams. By
employing the Hamilton-Jacobi method, we construct a boundary counter-term that
renders a renormalized action with a vanishing variation. We use this finite
action for the partition function in the semi-classical approximation. We
establish a consistent Thermodynamics, verified by the first law, across all
the black hole solutions presented, including the extreme case.
