  Due to their long mean free path, X-rays are expected to have an important
impact on cosmic reionization by heating and ionizing the IGM on large scales,
especially after simulations have suggested that Population III stars may form
in pairs at redshifts as high as 20 - 30. We use the Pop III distribution and
evolution from a self-consistent cosmological radiation hydrodynamics
simulation of the formation of the first galaxies and a simple Pop III X-ray
binaries model to estimate their X-ray output in a high density region larger
than 100 comoving (Mpc)$^3$. We then combine three different methods --- ray
tracing, a one-zone model, and X-ray background modeling --- to investigate the
X-ray propagation, intensity distribution, and long term effects on the IGM
thermal and ionization state. The efficiency and morphology of photo-heating
and photo-ionization are dependent on the photon energies. The sub-keV X-rays
only impact the IGM near the sources while the keV photons contribute
significantly to the X-ray background and heat and ionize the IGM smoothly. The
X-rays just below 1 keV are most efficient in heating and ionizing the IGM. We
find that the IGM might be heated to over 100 K by $z=10$ and the high density
source region might reach 10$^4$ K, limited by atomic hydrogen cooling. This
may be important for predicting the 21-cm neutral hydrogen signals. But, on the
other hand, the free electrons from X-ray ionizations are not enough to
contribute significantly to the optical depth of CMB to the Thomson scattering.
