We describe an experiment in which we have used a cold damping feedback mec
hanism to reduce the thermal noise of a mirror around its mechanical resona
nce frequency. The monitoring of the Brownian motion of the mirror allows o
ne to apply an additional viscous force without any extra thermal fluctuati
ons. This scheme has been experimentally implemented with the radiation pre
ssure of an intensity-modulated laser beam. Large noise reductions, up to 3
0 dB, have been obtained. We have also checked the mechanical response of t
he cold damped mirror, and monitored its transient evolution between the co
oled regime and the room-temperature equilibrium. A simple theoretical mode
l allows us to fully explain the experimental results. A possible applicati
on to the active cooling of the violin modes in a gravitational-wave interf
erometer is discussed.