  We compute holographic entanglement entropy for subregions of a BCFT thermal
state living on a nongravitating black hole background. The system we consider
is doubly holographic and dual to an eternal black string with an embedded
Karch-Randall brane that is parameterized by its angle. Entanglement islands
are conventionally expected to emerge at late times to preserve unitarity at
finite temperature, but recent calculations at zero temperature have shown such
islands do not exist when the brane lies below a critical angle. When working
at finite temperature in the context of a black string, we find that islands
exist even when the brane lies below the critical angle. We note that although
these islands exist when they are needed to preserve unitarity, they are
restricted to a finite connected region on the brane which we call the atoll.
Depending on two parameters -- the size of the subregion and the brane angle --
the entanglement entropy either remains constant in time or follows a Page
curve. We discuss this rich phase structure in the context of bulk
reconstruction.
