Isolated neutron stars are seen in x-rays through their nonthermal and/or surface thermal emissions. X-ray Multimirror Mission-Newton observations of the Geminga pulsar show a 43-electron volt spectrum from the whole neutron star surface, as well as a power-law component above 2 kiloelectron volts. In addition, we have detected a hot (170 electron volts) thermal emission from an ~60-meter-radius spot on the pulsar's surface. Such a thermal emission, only visible at selected phase intervals, may be coming from polar hot spot(s), long thought to exist as a result of heating from magnetospheric accelerated particles. It may provide the missing link between the x-ray and gamma-ray emission of the pulsar.