  Recently, a subset of starless cores whose thermal Jeans mass is apparently
overwhelmed by the mass of the core has been identified, e.g., the core {\small
L183}. In literature, massive cores such as this one are often referred to as
"super-Jeans cores". As starless cores are perhaps on the cusp of forming
stars, a study of their dynamics will improve our understanding of the
transition from the prestellar to the protostellar phase. In the present work
we use non-magnetic polytropes belonging originally to the family of the
Isothermal sphere. For the purpose, perturbations were applied to individual
polytropes, first by replacing the isothermal gas with a gas that was cold near
the centre of the polytrope and relatively warm in the outer regions, and
second, through a slight compression of the polytrope by raising the external
confining pressure. Using this latter configuration we identify thermodynamic
conditions under which a core is likely to remain starless. In fact, we also
argue that the attribute "super-Jeans" is subjective and that these cores do
not formally violate the Jeans stability criterion. On the basis of our test
results we suggest that gas temperature in a star-forming cloud is crucial
towards the formation and evolution of a core. Simulations in this work were
performed using the particle-based Smoothed Particle Hydrodynamics algorithm.
However, to establish numerical convergence of the results we suggest similar
tests with a grid-scheme, such as the Adaptive mesh refinement.
