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 L183. In the 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 this 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 secondly, 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.