Magnetars are neutron stars (NSs) with extreme magnetic fields of strength $5 times 10^{13}$ - $10^{15}$ G. They exhibit transient, highly energetic events, such as short X-ray flashes, bursts and giant flares, all of which are powered by their enormous magnetic energy. Quiescent magnetars have X-ray luminosities between $10^{29}$ and $10^{35}$ erg/s, and are further classified as either persistent or transient magnetars. Their X-ray emission is modulated with the rotational period of the NS, with a typical relative amplitude (so-called pulsed fraction) between 10-58 per cent, implying that the surface temperature is significantly non-uniform despite the high thermal conductivity of the stars crust. Here, we present the first 3D magneto-thermal MHD simulations of magnetars with strong toroidal magnetic fields. We show that these models, combined with ray propagation in curved space-time, accurately describe the light-curves of most transient magnetars in quiescence and allow us to further constrain their rotational orientation. We find that the presence of a strong toroidal magnetic field explains the observed asymmetry in the surface temperature, and is the main cause of the strong modulation of thermal X-ray emission in quiescence.
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