  The gauge sector of three-dimensional higher spin gravities can be formulated
as a Chern-Simons theory. In this context, a higher spin black hole corresponds
to a flat connection with suitable holonomy (smoothness) conditions which are
consistent with the properties of a generalized thermal ensemble. Building on
these ideas, we discuss a definition of black hole extremality which is
appropriate to the topological character of 3d higher spin theories. Our
definition can be phrased in terms of the Jordan class of the holonomy around a
non-contractible (angular) cycle, and we show that it is compatible with the
zero-temperature limit of smooth black hole solutions. While this notion of
extremality does not require supersymmetry, we exemplify its consequences in
the context of sl(3|2) + sl(3|2) Chern-Simons theory and show that, as usual,
not all extremal solutions preserve supersymmetries. Remarkably, we find in
addition that the higher spin setup allows for non-extremal supersymmetric
black hole solutions. Furthermore, we discuss our results from the perspective
of the holographic duality between sl(3|2) + sl(3|2) Chern-Simons theory and
two-dimensional CFTs with W_{(3|2)} symmetry, the simplest higher spin
extension of the N=2 super-Virasoro algebra. In particular, we compute
W_{(3|2)} BPS bounds at the full quantum level, and relate their semiclassical
limit to extremal black hole or conical defect solutions in the 3d bulk. Along
the way, we discuss the role of the spectral flow automorphism and provide a
conjecture for the form of the semiclassical BPS bounds in general N=2
two-dimensional CFTs with extended symmetry algebras.
