Cooling of neutron stars is calculated using an exact stellar evolution code. The full general relativistic version of the stellar structure equations are solved, with the best physical input available. For neutron stars with a stiff equation of state, it is found that the deviation from the isothermality in the interior is significant and that it takes at least a few thousand years to reach the isothermal state. By comparing theoretical and observational results, it is concluded that for Cas A, SN1006, and probably Tycho, standard cooling is inconsistent with the results from the Einstein Observatory, if neutron stars are assumed to be present in these objects. On the other hand, the detection points for RCW103 and the Crab are consistent with these theoretical results.
