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We describe the design and in--flight performance of the cryostat and the self-contained $^{3}$He refrigerator for the OLIMPO balloon--borne experiment, a spectrophotometer to measure the Sunyaev-Zel'dovich effect in clusters of galaxies. The $^{3}$He refrigerator provides the 0.3 K operation temperature for the four arrays of kinetic inductance detectors working in 4 bands centered at 150, 250, 350 and 460 GHz. The cryostat provides the 1.65 K base temperature for the $^{3}$He refrigerator, and cools down the reimaging optics and the filters chain at about 2 K. The integrated system was designed for a hold time of about 15 days, to achieve the sensitivity required by the planned OLIMPO observations, and successfully operated during the first long-duration stratospheric flight of OLIMPO in July 2018. The cryostat features two tanks, one for liquid nitrogen and the other one for liquid helium. The long hold time has been achieved by means of custom stiff G10 fiberglass tubes support, which ensures low thermal conductivity and remarkable structural stiffness; multi--layer superinsulation, and a vapour cooled shield, all reducing the heat load on the liquid helium tank. The system was tested in the lab, with more than 15 days of unmanned operations, and then in the long duration balloon flight in the stratosphere. In both cases, the detector temperature was below 300 mK, with thermal stability better than $\pm$ 0.5 mK. The system also operated successfully in the long duration stratospheric balloon flight.