Abstract The defining trait of magnetars, the most strongly magnetized neutron stars (NSs), is their transient activity in the X/ γ -bands. In particular, many of them undergo phases of enhanced emission, the so-called outbursts, during which the luminosity rises by a factor ∼10–1000 in a few hours to then decay over months/years. Outbursts often exhibit a thermal spectrum, associated with the appearance of hotter regions on the surface of the star, which subsequently change in shape and cool down. Here we simulate the unfolding of a sudden, localized heat injection in the external crust of an NS with a 3D magnetothermal evolution code, finding that this can reproduce the main features of magnetar outbursts. A full 3D treatment allows us to study for the first time the inherently asymmetric hot spots that appear on the surface of the star as the result of the injection and to follow the evolution of their temperature and shape. We investigate the effects produced by different physical conditions in the heated region, highlighting in particular how the geometry of the magnetic field plays a key role in determining the properties of the event.