Due to their long mean free paths, X-rays are expected to have global impacts on the properties of the intergalactic medium (IGM) by their large scale heating and ionizing processes. At high redshifts, X-rays from Population (Pop) III binaries might have important effects on cosmic reionization and the Lyα forest. As a continuation of our previous work on Pop III binary X-rays , we use the Pop III distribution and evolution from the Renaissance Simulations, a suite of self-consistent cosmological radiation hydrodynamics simulations of the formation of the first galaxies, to calculate the X-ray luminosity density and background over the redshift range 20 ≥ z ≥ 7.6. As we find that Pop III star formation continues at a low, nearly constant rate to the end of reionization, X-rays are being continuously produced at significant rates compared to other possible X-ray sources, such as AGNs and normal X-ray binaries during the same period of time. We estimate that Pop III binaries produce approximately 6 eV of energy in the X-rays per hydrogen atom. We calculate the X-ray background for different monochromatic photon energies. KeV X-rays redshift and accumulate to produce a strong X-ray background spectrum extending to roughly 500 eV. The X-ray background is strong enough to heat the IGM to ∼ 1000 K and to ionize a few percent of the neutral hydrogen. These effects are important for an understanding of the neutral hydrogen hyperfine transition 21-cm line signatures, the Lyα forest, and the Thomson optical depth to the CMB.