  In this work we reconsider the solution describing black holes surrounded by
a `quintessence'-like fluid. This geometry was introduced by Kiselev in 2003
and its physical source was originally modeled by an anisotropic fluid. We show
that the Kiselev geometry is actually an exact solution of the Einstein
equations coupled to nonlinear electrodynamics. More specifically, we show that
the Kiselev geometry becomes an exact solution in the context of power-Maxwell
electrodynamics, using either an electric ansatz or a magnetic one. In both
cases the physical source can be modeled by a power-Maxwell Lagrangian, albeit
with different powers corresponding to the electric or the magnetic charges. We
briefly investigate the motion of charged particles in this geometry. Finally,
we give the proper interpretation of the black-hole thermodynamics in this
context. Similarly to the Schwarzschild-de Sitter case, we note the presence of
the Schottky peaks in the heat capacity, signaling out the possibility of this
thermodynamic black hole system to function as a continuous heat machine.
