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What degrees of freedom contribute to the temperature of a gas?

Let's say we have a box of ideal gas. The temperature is the average kinetic energy of the particles and only includes translational degrees of freedom: velocity.

Now let's say we have a box of polyatomic gas instead, in which there are rotational degrees of freedom but no vibrational degrees of freedom. Is the temperature of gas still just the average translational kinetic energy, or do we have to add its average rotational energy?