  3C58 is a young Crab-like supernova remnant. Historical evidence strongly
suggests an association of the remnant with supernova SN 1181, which would make
3C58 younger than the Crab Nebula. Recent Chandra observations have identified
the young 65 ms pulsar J0205+6449 at its center, embedded in a compact nebula
which, we show here, appears to be confined by the pulsar wind termination
shock. We present new Chandra observations of this compact nebula and embedded
pulsar which set strong upper limits on thermal emission originating from the
neutron star surface. These limits fall far below predictions of standard
neutron star cooling, requiring the presence of exotic cooling processes in the
neutron star core.
