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 } \rightarrow - \infty ) .