  The origin of cosmic magnetic fields is an unsolved problem and
magnetogenesis could have occurred in the early Universe. We study the
evolution of such primordial magnetic fields across the cosmological
recombination epoch via 3D magnetohydrodynamic numerical simulations. We
compute the effective or net heating rate of baryons due to decaying magnetic
fields and its dependence on the magnetic field strength and spectral index. In
the drag-dominated regime ($z \gtrsim 1500$), prior to recombination, we find
no real heating is produced. Our simulations allow us to smoothly trace a new
transition regime ($600 \lesssim z \lesssim 1500$), where magnetic energy
decays, at first, into the kinetic energy of baryons. A turbulent velocity
field is built up until it saturates, as the net heating rate rises from a low
value at recombination to its peak towards the end of the transition regime.
This is followed by a turbulent decay regime ($z \lesssim 600$) where magnetic
energy dissipates via turbulent decay of both magnetic and velocity fields
while net heating remains appreciable and declines slowly. Both the peak of the
net heating rate and the onset of turbulent decay are delayed significantly
beyond recombination, by up to 0.5 Myr (until $z\simeq 600-700$), for
scale-invariant magnetic fields. We provide analytic approximations and present
numerical results for a range of field strengths and spectral indices,
illustrating the redshift-dependence of dissipation and net heating rates.
These can be used to study cosmic microwave background constraints on
primordial magnetic fields.
