  The negative nature of the heat capacity $C_V$ of thermodynamically isolated
self-gravitating systems is rediscussed in the framework of a non-extensive
kinetic theory. It is found that the dependence of $C_V$ on the non-extensive
parameter $q$ gives rise to a negative branch with the critical value
corresponding to $q = 5/3$ ($C_V\to - \infty$).
