RX J0720.4-3125 has recently been identified as a pulsating soft X-ray source in the ROSAT all-sky survey with a period of 8.391 s. Its spectrum is well characterized by a black-body with a temperature of 8 \times 10 ^ { 5 } K. We propose that the radiation from this object is thermal emission from a cooling neutron star . For this black-body temperature we can obtain a robust estimate of the object ’ s age of \sim 3 \times 10 ^ { 5 } yr , yielding a polar field \sim 10 ^ { 14 } G for magnetic-dipole spin down and a value of { \dot { P } } compatible with current observations .