Internal energy question

The question posed is simple and well-formulated, but did not receive a response in 880 days, which surprises me.
What makes this question interesting is, that it raises the question whether the heat capacity (proportionality between U and T, ie dU/dT) can be spit in a kinetic energy part and a potential energy part, and whether the latter part is zero.
Specially for solids it seems evident that both heat-capacities should be positive, but it has to be worked out quantitatively.
I would say the answer to the question as posed is no.