  We study the critical velocity of a Bose-condensed gas in a moving
one-dimensional (1D) optical lattice potential at finite temperatures. Solving
the Gross-Pitaeavskii equation and the Bogoliubov equations, within the Popov
approximation, we calculate the Bogoliubov excitations with varying lattice
velocity. From the condition of the negative excitation energy, we determine
the critical velocity as a function of the lattice depth and the temperature.
We find that the critical velocity decreases rapidly with increasing the
temperature; this result is consistent with the experimental observations.
Moreover, the critical velocity shows a rapid decrease with increasing lattice
depth. This tendency is much more significant than in the previous works
ignoring the effect of thermal excitations in the radial direction.
