The invention relates to a directable magnetic mount (10) for a light emitter (20). The invention also relates to a light source (200), to a base (40) and to an illumination system (100). The directable magnetic mount comprises interface means (30) configured for conducting thermal energy away from the light emitter to a heat sink (40), and comprises a magnetic connector (50) configured for magnetically connecting the directable magnetic mount to the base. The magnetic connector is configured for thermally interconnecting the interface means and the heat sink. The interface means is configured for being thermally connected to the heat sink at a plurality of orientations of the interface means with respect to the heat sink. Each of the plurality of orientations of the interface means comprises a different emission direction of the light emitter.The effect of the measures according to the invention is that it enables to omit the need for a heat sink in the light source which enables to reduce the size of the light source while also allowing to reposition and redirect the light emitted from the illumination system.