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 isrnan inverted power law with slope γ - 1～-0.2, in both models. However, at fixed density there is up to orderrnunity 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 Lyα absorption in high-redshift quasar spectra.
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