  We investigate the effect of a cosmological constant on the gravothermal
catastrophe in the Newtonian limit. A negative cosmological constant acts as a
thermodynamic `destabilizer'. The Antonov radius gets smaller and the
instability occurs, not only for negative but also for positive energy values.
A positive cosmological constant acts as a `stabilizer' of the system, which,
in this case, exhibits a novel `reentrant behaviour'. In addition to the
Antonov radius we find a second critical radius, where an `inverse Antonov
transition' occurs; a series of local entropy maxima is restored.
