Solid state laser refrigeration can cool optically levitated nanocrystals in an optical dipole trap, allowing for internal temperature control by mitigating photothermal heating. This work demonstrates cooling of ytterbium-doped cubic sodium yttrium fluoride nanocrystals to 252 K on average with the most effective crystal cooling to 241 K. The amount of cooling increases linearly with the intensity of the cooling laser and is dependent on the pressure of the gas surrounding the nanocrystal. Cooling optically levitated nanocrystals allows for crystals prone to heating to be studied at lower pressures than currently achievable and for temperature control and stabilization of trapped nanocrystals.