= Solution
At low <temperature>, the upper orientation has negligible <Boltzmann weight>, whereas at high <temperature> all three orientations become equally probable. Consequently
$$
\boxed{U(0)=-N\varepsilon,\qquad U(\infty)=-N\varepsilon+\frac{N\delta}{3}.}
$$
The high-temperature limit is a finite arithmetic mean of three available one-site <energy levels>. It is not an unbounded translational or rotational <equipartition> contribution: the prescribed site model has only three states per molecule. Their common binding offset can keep this limiting <internal energy> negative without any inconsistency.
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