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Yes. For an ideal gas the internal energy which is a combination of both Kinetic(K)and Potential(U) energy is related to temperature in the following way.

E = K+U = 3/2 * R * T

However since there is no particle integration in an ideal gas the potential energy is 0 thus:

E = K = 3/2 *R*T => K ~ T

So the kinetic energy of the system is directly proportional to the temperature. If T goes up, so does K.

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