  We study the impact of inhomogeneous hydrogen reionization on the thermal
evolution of the intergalactic medium (IGM) using hydrodynamic + radiative
transfer simulations where reionization is completed either early (z ~ 9) or
late (z ~ 6). In general, we find that low-density gas near large-scale
overdensities is ionized and heated earlier than gas in the large-scale,
underdense voids. Furthermore, at a later time the IGM temperature is inversely
related to the reionization redshift because gas that is heated earlier has
more time to cool through adiabatic expansion and Compton scattering. Thus, at
the end of reionization the median temperature-density relation is an inverted
power-law with slope gamma-1 ~ -0.2, in both models. However, at fixed density,
there is up to order unity scatter in the temperature due to the distribution
of reionization redshifts. Because of the complex equation-of-state, the
evolved IGM temperature-density relations for the redshift range 4 < z < 6 can
still have significant curvature and scatter. These features must be taken into
account when interpreting the Lyman alpha absorption in high redshift quasar
spectra.
