= Solution
At low temperature, $x=\varepsilon/(k_BT)\gg1$, so the denominator in the exact expression approaches one:
$$
\boxed{\alpha\sim\frac{3\varepsilon}{k_BT^2}
e^{-\varepsilon/(k_BT)}\longrightarrow0\quad(T\to0)}.
$$
The exponential suppression dominates the $T^{-2}$ factor. Almost all particles remain in the ground state, so very little volume change is thermally accessible.
At high temperature, $e^{-x}\to1$, and therefore
$$
\boxed{\alpha\sim\frac{3\varepsilon}{16k_BT^2}
\longrightarrow0\quad(T\to\infty)}.
$$
The excited fraction has already approached $3/4$, so further heating barely changes it. Both limits are consistent with a bounded <two-level system>; the high-temperature vanishing does not imply that ordinary materials cease expanding when additional levels or other mechanisms become accessible.
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