We synthesize, optically trap, and rotate individual nanovaterite crystals with a mean particle radius of 423 nm. Rotation rates of up to 4.9 kHz in heavy water are recorded . Laser-induced heating due to residual absorption of the nanovaterite particle results in the superlinear behavior of the rotation rate as a function of trap power. A finite element method based on the Navier-Stokes model for the system allows us to determine the residual optical absorption coefficient for a trapped nanovaterite particle. This is further confirmed by the theoretical model. Our data reveal that the nanoparticle experiences a different Stokes drag torque or force depending on whether we consider rotational or translational motion, which is in a good agreement with the theoretical prediction of the rotational hot Brownian motion . The data allow us to determine the correction factors for the local viscosity for both the rotational and translational motion of the nanoparticle. The use of nanovaterite particles opens up new studies for levitated optomechanics in vacuum [3-6] as well as microrheological properties of cells or biological media . For these latter studies, nanovaterite offers prospects of microviscosity measurements in ultrasmall volumes and, due to its size, potentially simpler uptake by cellular media .