How to understand the negative specific heat of a massless Majorana fermion in one dimension?

Let us consider a massless Majorana fermion on a ring of length $L$ with a periodic boundary condition at a temperature $T$.
Then the conformal field theory calculation tells us that the quantum partition function of this single Majorana is ($k_text{B}equiv1$)
begin{eqnarray}
Z(T,L)=chi_{1/16}(tau)chi^*_{1/16}(tau)|_{tau=i/(LT)},
end{eqnarray}
where $chi_{h}(tau)$ is the Virasoro character of the primary field with conformal dimension $h$.
Then when the system size is large $LTgg1$, the asymptotic behavior of the partition function is
begin{eqnarray}
Z(T,L)&approx&expleft{frac{pi LT}{6}[c-12(h+bar{h})]right},
end{eqnarray}
where $h=bar{h}=1/16$ namely the lowest value of the Virasoro generators $L_0$ and $bar{L}_0$ of the massless Majorana with a central charge $c=1/2$.

Therefore, we can obtain the specific heat per unit length as
begin{eqnarray}
c_v&=&frac{1}{L}Tfrac{partial^2}{partial T^2}[Tln(Z(T,L))]
&=&frac{pi T}{3}(c-12h-12bar{h})
&=&-frac{pi T}{3}
&<&0text{ (when $T>0$)}.
end{eqnarray}
My question is how to understand this negative specific heat and does it mean that Majorana fermion is thermally unstable at all at any finite temperature?