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 currently available. For neutron stars with a stiff equation of state, we find 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 the most recent theoretical and observational results, we conclude 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.