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Kinetic energy of a particle (atom or molecule) within a substance is proportional to the temperature of the substance.

Specifically, the equation is KE=3kT/2, where k is Boltzmann's constant and T is the absolute temperature, normally measured in degrees Kelvin. KE is the average translational kinetic energy of the particles in the substance.

Caveat: At extremely low temperatures this is modified by quantum mechanics.
At extremely high velocities this is modified by the special theory of relativity.
Finally, this answer discusses translational kinetic energy, but a similar discussion applies to vibrational and rotational kinetic energy as well and they (subject to quantum theory and relativity) have a similar property of being proportional to temperature.

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