  Heat engines used to output useful work have important practical
significance, which, in general, operate between heat baths of infinite size
and constant temperature. In this paper we study the efficiency of a heat
engine operating between two finite-size heat sources with initial temperature
differences. The total output work of such heat engine is limited due to the
finite heat capacity of the sources. We investigate the effects of different
heat capacity characteristics of the sources on the heat engine's efficiency at
maximum work (EMW) in the quasi-static limit. In addition, we study the
efficiency of the engine working in finite-time with maximum power of each
cycle is achieved and find the efficiency follows a simple universality as
$\eta=\eta_{\mathrm{C}}/4+O\left(\eta_{\mathrm{C}}^{2}\right)$. Remarkably,
when the heat capacity of the heat source is negative, such as the black holes,
we show that the heat engine efficiency during the operation can surpass the
Carnot efficiency determined by the initial temperature of the heat sources. It
is further argued that the heat engine between two black holes with vanishing
initial temperature difference can be driven by the energy fluctuation. The
corresponding EMW is proved to be $\eta_{\mathrm{EMW}}=2-\sqrt{2}$, which is
two time of the maximum energy release rate
$\mu=\left(2-\sqrt{2}\right)/2\approx0.29$ of two black hole emerging process
obtained by S. W. Hawking.
