We study the fluctuation-electromagnetic interaction and dynamics of a small spinning polarizable particle moving with a relativistic velocity in a vacuum background of arbitrary temperature. Using the standard formalism of the fluctuation electromagnetic theory, a complete set of equations describing the decelerating tangential force, the components of the torque and the intensity of nonthermal and thermal radiation is obtained along with equations describing the dynamics of translational and rotational motion, and the kinetics of heating. An interplay between various parameters is discussed. Numerical estimations for conducting particles were carried out using MATHCAD code. In the case of zero temperature of a particle and background radiation, the intensity of radiation is independent of the linear velocity, while the angular velocity orientation and the linear velocity value are independent of time. In the case of a finite background radiation temperature, the angular velocity vector tends to be oriented perpendicularly to the linear velocity vector. The particle temperature relaxes to a quasistationary value depending on the background radiation temperature, the linear and angular velocities, whereas the intensity of radiation depends on the background radiation temperature, the angular and linear velocities. The time of thermal relaxation is much less than the time of angular deceleration, while the latter time is much less than the time of linear deceleration.