  We examine the evolution of the phase diagram of the low-density
intergalactic medium (IGM) during the Epoch of Reionization in simulation boxes
with varying reionization histories from the Cosmic Reionization on Computers
project. The PDF of gas temperature at fixed density exhibits two clear modes:
a warm and cold temperature mode, corresponding to the gas inside and outside
of ionized bubbles. We find that the transition between the two modes is
"universal" in the sense that its timing is accurately parameterized by the
value of the volume-weighted neutral fraction for any reionization history.
This "universality" is more complex than just a reflection of the fact that
ionized gas is warm and neutral gas is cold: it holds for the transition at a
fixed value of gas density, and gas at different densities transitions from the
cold to the warm mode at different values of the neutral fraction, reflecting a
non-trivial relationship between the ionization history, the evolving gas
density PDF, and the spectrum of ionizing radiation. Furthermore, the
"emergence" of the tight temperature-density relation in the warm mode is also
approximately "universally" controlled by the volume-weighted neutral fraction
for any reionization history. In particular, the "emergence" of the
temperature-density relation (as quantified by the rapid decrease in its width)
occurs when the neutral fraction is $10^{-4}\lesssim X_\mathrm{HI}
\lesssim10^{-3}$ for any reionization history. Our results indicate that the
neutral fraction is a primary quantity controlling the various properties of
the temperature-density relation, regardless of reionization history.
