  The friction force acting on a small neutral particle during relativistic
motion relative to the blackbody radiation is calculated in the framework of
fluctuation electrodynamics. It is shown that the particle acceleration is
determined by the friction force in the particle rest reference frame
($K^{\prime}$-frame) which in general is not equal to the friction force in the
frame of the blackbody radiation ($K$-frame). The difference between the
friction forces in the different frames is connected with the change of the
rest mass of a particle due to the absorption and emission of radiation. The
friction force in the $K^{\prime}$-frame is determined only by the interaction
of a particle with the blackbody radiation. In the $K$-frame the interaction of
a particle with its own thermal radiation also contributes to the friction
force. For the steady state temperature of a particle the friction forces in
the $K^{\prime}$-and $K$-frames are equal. For an atom the blackbody friction
is determined by the electronic linewidth broadening which is calculated
considering the interaction of an atom with its own radiation. In the
ultrarelativistic case ($1-\beta\rightarrow 0$) for an atom the friction force
diverges as $(1-\beta)^{-3}$ and the (average) temperature of an atom
$T_2\approx (1-\beta)^{-3/8}T_1$, where $T_1$ is the temperature of the
blackbody radiation and $\beta=V/c$. Controversies in the theory of the
blackbody friction are discussed.
