Structure in the Universe grew through gravitational instability from very smooth initial conditions. Energy conservation requires that the growing negative potential energy of these structures is balanced by an increase in kinetic energy. A fraction of this is converted into heat in the collisional gas of the intergalactic medium. Using a toy model of gravitational heating we attempt to link the growth of structure in the Universe and the average temperature of this gas. We find that the gas

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... rapidly heated from collapsing structures at around z ∼ 10, reaching a temperature > 10^6K today, depending on some assumptions of our simplified model. Before that there was a cold era from z∼100 to ∼10 in which the matter temperature is below that of the Cosmic Microwave Background.