  One of the greatest challenges in solar physics is understanding the heating
of the Sun's corona. Most theories for coronal heating postulate that free
energy in the form of magnetic twist/stress is injected by the photosphere into
the corona where the free energy is converted into heat either through
reconnection or wave dissipation. The magnetic helicity associated with the
twist/stress, however, is expected to be conserved and appear in the corona. In
previous work we showed that helicity associated with the small-scale twists
undergoes an inverse cascade via stochastic reconnection in the corona, and
ends up as the observed large-scale shear of filament channels. Our ``helicity
condensation'' model accounts for both the formation of filament channels and
the observed smooth, laminar structure of coronal loops. In this paper, we
demonstrate, using helicity- and energy-conserving numerical simulations of a
coronal system driven by photospheric motions, that the model also provides a
natural mechanism for heating the corona. We show that the heat generated by
the reconnection responsible for the helicity condensation process is
sufficient to account for the observed coronal heating. We study the role that
helicity injection plays in determining coronal heating and find that,
crucially, the heating rate is only weakly dependent on the net helicity
preference of the photospheric driving. Our calculations demonstrate that
motions with 100\% helicity preference are least efficient at heating the
corona; those with 0\% preference are most efficient. We discuss the physical
origins of this result and its implications for the observed corona.
