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abstract: 'Recent observations of the central compact object in the Kesteven 79 supernova remnant show that this neutron star (NS) has a weak dipole magnetic field (a few$\times 10^{10}$G) but an anomalously large ($\sim 64\%$) pulse fraction in its surface X-ray emission. We explore the idea that a substantial sub-surface magnetic field exists in the NS crust, which produces diffuse hot spots on the stellar surface due to anisotropic heat conduction, and gives rise to the observed X-ray pulsation. We develop a general-purpose method, termed “Temperature Template with Full Transport” (TTFT), that computes the synthetic pulse profile of surface X-ray emission from NSs with arbitrary magnetic field and surface temperature distributions, taking into account magnetic atmosphere opacities, beam pattern, vacuum polarization, and gravitational light bending. We show that a crustal toroidal magnetic field of order a few$\times 10^{14}$G or higher, varying smoothly across the crust, can produce sufficiently distinct surface hot spots to generate the observed pulse fraction in the Kes 79 NS. This result suggests that substantial sub-surface magnetic fields, much stronger than the “visible” dipole fields, may be buried in the crusts of some young NSs, and such hidden magnetic fields can play an important role in 