  The thermal fluctuation of mirror surfaces is the fundamental limitation for
interferometric gravitational wave (GW) detectors. Here, we experimentally
demonstrate for the first time a reduction in a mirror's thermal fluctuation in
a GW detector with sapphire mirrors from the Cryogenic Laser Interferometer
Observatory at 17\,K and 18\,K. The detector sensitivity, which was limited by
the mirror's thermal fluctuation at room temperature, was improved in the
frequency range of 90\,Hz to 240\,Hz by cooling the mirrors. The improved
sensitivity reached a maximum of $2.2 \times
10^{-19}\,\textrm{m}/\sqrt{\textrm{Hz}}$ at 165\,Hz.
