Abstract
Ultramagnetized neutron stars or magnetars have been invoked to explain several astrophysical phenomena. We examine how the magnetic field of a magnetar will decay over time and how this decay affects the cooling of the object. We find that for sufficiently strong nascent fields, field decay alters the cooling evolution significantly relative to similarly magnetized neutron stars with constant fields. As a result, old magnetars can be expected to be bright in the soft X-ray band. The soft X-ray source RXJ~0720.4$-$3125 may well be the nearest such old magnetar.