  Non-thermal electron acceleration via magnetic reconnection is thought to
play an important role in powering the variable X-ray emission from radiatively
inefficient accretion flows around black holes. The trans-relativistic regime
of magnetic reconnection, where the magnetization $\sigma$, defined as the
ratio of magnetic energy density to enthalpy density, is $\sim 1$, is
frequently encountered in such flows. By means of a large suite of
two-dimensional particle-in-cell simulations, we investigate electron and
proton acceleration in the trans-relativistic regime. We focus on the
dependence of the electron energy spectrum on $\sigma$ and the proton $\beta$
(i.e., the ratio of proton thermal pressure to magnetic pressure). We find that
the electron spectrum in the reconnection region is non-thermal and can be
generally modeled as a power law. At $\beta \lesssim 3 \times 10^{-3}$, the
slope, $p$, is independent of $\beta$ and it hardens with increasing $\sigma$
as $p\simeq 1.8 +0.7/\sqrt{\sigma}$. Electrons are primarily accelerated by the
non-ideal electric field at X-points, either in the initial current layer or in
current sheets generated in between merging magnetic islands. At higher values
of $\beta$, the electron power law steepens for all values of $\sigma$. At
values of $\beta$ near $\beta_{\rm max}\approx1/4\sigma$, when both electrons
and protons are relativistically hot prior to reconnection, the spectra of both
species display an additional component at high energies, containing a few
percent of particles. These particles are accelerated via a Fermi-like process
by bouncing in between the reconnection outflow and a stationary magnetic
island. We provide an empirical prescription for the dependence of the
power-law slope and the acceleration efficiency on $\beta$ and $\sigma$, which
can be used in global simulations of collisionless accretion disks.
