  It has been established that the low frequency quasi-localized modes of
amorphous solids at zero temperature exhibit universal density of states,
depending on the frequencies as $D(\omega) \sim \omega^4$. It remains an open
question whether this universal law extends to finite temperatures. In this
Letter we show that well quenched model glasses at temperatures as high as
$T_g/3$ possess the same universal density of states. The only condition
required is that {\em average} particle positions stabilize before thermal
diffusion destroys the cage structure of the material. The universal density of
quasi-localized low frequency modes refers then to vibrations around the
thermally averaged configuration of the material.
