  We study the effect of thermal and quantum fluctuations on the dynamical
response of a one-dimensional strongly-interacting Bose gas in a tight atomic
waveguide. We combine the Luttinger liquid theory at arbitrary interactions and
the exact Bose-Fermi mapping in the Tonks-Girardeau-impenetrable-boson limit to
obtain the dynamic structure factor of the strongly-interacting fluid at finite
temperature. Then, we determine the drag force felt by a potential barrier
moving along the fluid in the experimentally realistic situation of finite
barrier width and temperature.
