  We study the quantum Vavilov-Cherenkov (QVC) radiation and quantum friction
occurring during motion of a small neutral particle parallel to a transparent
dielectric plate with the refractive index $n$. This phenomenon occurs above
the threshold velocity $v_c=c/n$. The particle acceleration and rate of heating
are determined by the friction force and heating power in the rest reference
frame of the particle. We calculate these quantities starting from the
expressions for the friction force and the radiative energy transfer in the
plate-plate configuration, assuming plate at the rest in the \textit{lab} frame
rarefied. Close to the light velocity there is a big difference between the
friction force and the radiation power in the rest frame of a particle and in
the \textit{lab} reference frame. This difference is connected with the change
of the rest mass of the particle due to absorption of radiation. Close to the
threshold velocity the decrease of the kinetic energy of the particle is
determined mainly by radiation power in in the \textit{lab} frame. However,
close to the light velocity it is determined also by the heating power for the
particle. We establish the connections between the quantities in the different
reference frames. For a nanoparticle the QVC radiation intensity can be
comparable to classical one. We discuss the possibility to detect QVC
radiation.
