  We have considered the thermal equilibrium in pre-protostellar cores in the
approximation where the dust temperature is independent of interactions with
the gas and where the gas is heated both by collisions with dust grains and
ionization by cosmic rays. We have then used these results to study the
stability of cores in the limit where thermal pressure dominates over magnetic
field and turbulence. We find that for cores with characteristics similar to
those observed, the gas and dust temperatures are coupled in the core interior.
As a consequence, the gas temperature like the dust temperature decreases
towards the center of these objects. The density structure computed taking into
account such deviations from isothermality are not greatly different from that
expected for an isothermal Bonnor-Ebert sphere. It is impossible in the
framework of these models to have a stable equilibrium core with mass above
about 5 solar masses and column density compatible with observed values. We
conclude from this that observed high mass cores are either supported by
magnetic field or turbulence or are already in a state of collapse. Lower mass
cores on the other hand have stable states and we conclude that the much
studied object B68 may be in a state of stable equilibrium if the internal gas
temperature is computed in self-consistent fashion. Finally we note that in
molecular clouds such as Ophiuchus and Orion with high radiation fields and
pressures, gas and dust temperatures are expected to be well coupled and hence
one expects temperatures to be relatively high as compared to low pressure
clouds like Taurus.
