  Many low-mass X-ray binary (LMXB) systems are observed to contain rapidly
spinning neutron stars. The spin frequencies of these systems may be limited by
the emission of gravitational waves. This can happen if their mass distribution
is sufficiently non-axisymmetric. It has been suggested that such `mountains'
may be created via temperature non-axisymmetries, but estimates of the likely
level of temperature asymmetry have been lacking. To remedy this, we examine a
simple symmetry breaking mechanism, where an internal magnetic field perturbs
the thermal conductivity tensor, making it direction-dependent. We find that
the internal magnetic field strengths required to build mountains of the
necessary size are very large, several orders of magnitude larger than the
inferred external field strengths, pushing into the regime where our assumption
of the magnetic field having a perturbative effect on the thermal conductivity
breaks down. We also examine how non-axisymmetric surface temperature profiles,
as might be caused by magnetic funnelling of the accretion flow, lead to
internal temperature asymmetries, but find that for realistic parameters the
induced non-axisymmetries are very small. We conclude that, in the context of
this work at least, very large internal magnetic fields are required to
generate mountains of the necessary size.

High Energy Astrophysical Phenomena;General Relativity and Quantum Cosmology