We have cooled liquid He-3 contained in a 98% open aerogel sample surrounded by bulk superfluid He-3-B at zero pressure to below 120 mu K. The aerogel sample is placed in a quasiparticle blackbody radiator cooled by a Lancaster-style nuclear cooling stage to similar to 200 mu K. We monitor the temperature of the He-3 inside the blackbody radiator using a vibrating wire resonator. We find that reducing the magnetic field on the aerogel sample causes substantial cooling of all the superfluid inside the blackbody radiator. We believe this is due to the demagnetization of the solid He-3 layers on the aerogel strands. This system has potential for achieving extremely low temperatures in the confined fluid.