Asymptotics of statistic characteristics of unharmonic oscillator

Let $T$, $F(T)$, $\overline E(T)$ and $S(T)$ denote the temperature, energy, mean energy and entropy of an equilibrium system, respectively. Under some conditions we find the asymptotic behaviour of $F(T)$, $\overline E(T)$ and $S(T)$ for the cases where either $T\to\infty$ or $T\to 0$. We compare the obtained results in quantum and classical cases.