  Black hole-torus systems from compact binary mergers are possible engines for
gamma-ray bursts (GRBs). During the early evolution of the post-merger remnant,
the state of the torus is determined by a combination of neutrino cooling and
magnetically-driven heating processes, so realistic models must include both
effects. In this paper, we study the post-merger evolution of a magnetized
black hole-neutron star binary system using the Spectral Einstein Code (SpEC)
from an initial post-merger state provided by previous numerical relativity
simulations. We use a finite-temperature nuclear equation of state and
incorporate neutrino effects in a leakage approximation. To achieve the needed
accuracy, we introduce improvements to SpEC's implementation of
general-relativistic magnetohydrodynamics (MHD), including the use of
cubed-sphere multipatch grids and an improved method for dealing with
supersonic accretion flows where primitive variable recovery is difficult. We
find that a seed magnetic field triggers a sustained source of heating, but its
thermal effects are largely cancelled by the accretion and spreading of the
torus from MHD-related angular momentum transport. The neutrino luminosity
peaks at the start of the simulation, and then drops significantly over the
first 20\,ms but in roughly the same way for magnetized and nonmagnetized
disks. The heating rate and disk's luminosity decrease much more slowly
thereafter. These features of the evolution are insensitive to grid structure
and resolution, formulation of the MHD equations, and seed field strength,
although turbulent effects are not fully converged
