A rigid object having negative heat capacity and positive temperature $T$ is placed inside a cavity whose walls are maintained at positive temperature $T_{\mathrm{R}}$. Explain what happens when $T>T_{\mathrm{R}}$ and when $T<T_{\mathrm{R}}$. Modelling the object as a rigid box containing a self-gravitating gas which initially only fills part of the box, explain what prevents $T$ from either reaching absolute zero or increasing indefinitely.