  This paper describes the numerical evolution of an $N$-body system with a
slight ``temperature inversion''; i.e. the maximum velocity dispersion occurs
not at the centre but further out. Fluid models predict that the core of such a
system expands on a time-scale of thousands of central relaxation times, and
here this behaviour is qualitatively confirmed for an $N$-body system of over
3000 bodies. With certain qualifications, this demonstrates the existence in
N-body systems of one of the fundamental mechanisms which, in fluid models,
drive the gravothermal oscillations discovered by Bettwieser & Sugimoto.
