  We consider holographic duals of $2$-dimensional conformal field theories in
the presence of a boundary, interface, defect and/or junction, referred to
collectively as BCFTs. In general, the presence of a boundary reduces the
$SO(2,2)$ conformal symmetry to $SO(2,1)$ and the dual geometry is realized as
a warped product of the form $AdS_2 \times {\cal M}$, where ${\cal M}$ is not
compact. In particular, it will contain points where the warp factor of the
$AdS_2$ space diverges, leading to asymptotically $AdS_3$ regions. We show that
the $AdS_2$ space-time may always be replaced with an $AdS_2$-"black-hole"
space-time. We argue the resulting geometry describes the BCFT at finite
temperature. To motivate this claim, we compute the entanglement entropy
holographically for a segment centered around the defect or ending on the
boundary and find agreement with a known universal formula.
