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 t
he core of such a system expands on a time-scale of thousands of centr
al relaxation times, and here this behaviour is qualitatively confirme
d for an N-body system of over 3000 bodies. With certain qualification
s, this demonstrates the existence in N-body systems of one of the fun
damental mechanisms that, in fluid models, drive the gravothermal osci
llations discovered by Bettwieser and Sugimoto.