  We investigate the heat properties of charged AdS black holes in the
Gauss-Bonnet gravity coupled with nonlinear electrodynamics. We consider the
thermodynamics of black holes from the perspective of heat capacity and show
that the nonlinear electrodynamics can be helpful to improve the thermodynamic
stability of black holes. We perform a two-dimensional description in order to
reproduce the Hawking temperature, which confirms that the Hawking temperature
has an intrinsic topological nature and holds for a higher dimensional
spherically symmetric spacetime. We also analyze the Maxwell equal area law and
coexistence curve, and find the existence of van der Waals-like phase
transitions based on critical exponents. Moreover, we deal with a charged AdS
black hole in the Gauss-Bonnet gravity coupled with nonlinear electrodynamics
as a working material to study holographic heat engines and obtain an exact
expression for the efficiency of a rectangular engine cycle. We then discuss
the effects of nonlinear electrodynamics and Gauss-Bonnet couplings on the
rectangular engine cycle and compare the efficiency of this cycle with that of
the Carnot cycle.
