Quote by aaaa202
hmm okay, but aren't you assuming that energy and temperature are proportional?

Yes. For an ideal monatomic gas, U= 3 N (kT/2) where U= total energy, N=total particles. For d degrees of freedom, U=d N (kT/2).
For the general situation, the "degrees of freedom" become a function of temperature, and then it may not be proportional.