  The grand canonical ensemble formulation of the van der Waals equation of
state that includes the effects of Bose statistics is applied to an equilibrium
system of interacting pions. If the attractive interaction between pions is
large enough, a limiting temperature $T_0$ emerges, i.e., no thermodynamical
equilibrium is possible at $T>T_0$. The system pressure $p$, particle number
density $n$, and energy density $\varepsilon$ remain finite at $T=T_0$, whereas
for $T$ near $T_0$ both the specific heat $C=d\varepsilon/dT$ and the scaled
variance of particle number fluctuations $\omega[N]$ are proportional to
$(T_0-T)^{-1/2}$ and, thus, go to infinity at $T\rightarrow T_0$. The limiting
temperature corresponds also to the softest point of the equation of state,
i.e., the speed of sound squared $c_s^2=dp/d\varepsilon$ goes to zero as
$(T_0-T)^{1/2}$. Very similar thermodynamical behavior takes place in the
Hagedorn model for the special choice of a power, namely $m^{-4}$, in the
pre-exponential factor of the mass spectrum $\rho(m)$.
