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.
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