Mesoporous amorphous-crystalline nanopowders of BaF_2 with the specific surface area up to 34.8 m^2/g were obtained using evaporation by a pulsed electron beam in vacuum. Influence of the thermal annealing of the BaF_2 nanoparticles in air at the temperatures from 200 to 900°C on the size and morphology of the particles and changes in their magnetic and luminescent properties was studied. The paramagnetic response of the BaF_2 nanopowder was found to transform to the ferromagnetic response after annealing at 900°C. The appearance and transformation of the magnetic response in nanopowders made of BaF_2, which is diamagnetic as the bulk material, are ascribed to the appearance of radiation-induced and structural defects during the synthesis process by pulsed electron-beam evaporation.