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ABSTRACT We examine the evolution of the phase diagram of the low-density intergalactic medium during the Epoch of Reionization in simulation boxes with varying reionization histories from the Cosmic Reionization on Computers project. The probability density function (PDF) of gas temperature at fixed density exhibits two clear modes: a warm and a 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 parametrized 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 and the evolving gas density PDF. 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 ≲ XH i ≲ 10−3 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.