  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 x 10^{10} G) but an anomalously large (~ 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 x 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 their
observational manifestations. The general TTFT tool we have developed can also
be used for studying radiation from other magnetic NSs.
