  We study the heat capacity of a static system of self-gravitating radiations
analytically in the context of general relativity. To avoid the complexity due
to a conical singularity at the center, we excise the central part and replace
it with a regular spherically symmetric distribution of matters of which
specifications we are not interested in. We assume that the mass inside the
inner boundary and the locations of the inner and the outer boundaries are
given. Then, we derive a formula relating the variations of physical parameters
at the outer boundary with those at the inner boundary. Because there is only
one free variation at the inner boundary, the variations at the outer boundary
are related, which determines the heat capacity. To get an analytic form for
the heat capacity, we use the thermodynamic identity $\delta S_{\rm rad} =
\beta \delta M_{\rm rad}$ additionally, which is derived from the variational
relation of the entropy formula with the restriction that the mass inside the
inner boundary does not change. Even if the radius of the inner boundary of the
shell goes to zero, in the presence of a central conical singularity, the heat
capacity does not go to the form of the regular sphere. An interesting
discovery is that another legitimate temperature can be defined at the inner
boundary which is different from the asymptotic one $\beta^{-1}$.
