The Universe is opaque to extragalactic very high-energy gamma rays (VHEGRs, E>100 GeV) because they annihilate and pair produce on the extragalactic background light. The resulting ultra-relativistic pairs are assumed to lose energy through inverse Compton scattering of CMB photons. In Broderick et al. (2011, Paper I of this three paper series), we argued that instead powerful plasma instabilities in the ultra-relativistic pair beam dissipate the kinetic energy of the TeV-generated pairs locally, heating the intergalactic medium (IGM). Here, we explore the effect of this heating upon the thermal history of the IGM. We collate the observed extragalactic VHEGR sources to determine a local VHEGR heating rate and correct for the pointed nature of VHEGR observations using Fermi observations of high and intermediate peaked BL Lacs. Because the local extragalactic VHEGR flux is dominated by TeV blazars, we tie the TeV blazar luminosity density to the quasar luminosity density, and produce a VHEGR heating rate as a function of redshift. This heating is relatively homogeneous for z<~4 with increasing spatial variation at higher redshift (order unity at z~6). This new heating process dominates photoheating at low redshift and the inclusion of TeV blazar heating qualitatively and quantitatively changes the structure and history of the IGM. TeV blazars produce a uniform volumetric heating rate that is sufficient to increase the temperature of the mean density IGM by nearly an order of magnitude, and at low densities by substantially more, naturally producing an inverted equation of state inferred by observations of the Ly-alpha forest, a feature that is difficult to reconcile with standard reionization models. Finally, we close with a discussion on the possibility of detecting this hot low-density IGM, but find that such measurements are currently not feasible. (abridged)
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