  We study the properties of fully-heavy baryons in the vacuum and the hot QCD
medium, which is created in relativistic heavy-ion collisions. Masses and wave
functions of $\Omega_{ccc}$, $\Omega_{ccb}$, $\Omega_{bbc}$, and $\Omega_{bbb}$
up to the second radial excited states are obtained by solving the three-body
Schr\"odinger equation with Hyperspherical Harmonics method. With parameters
completely fixed by fitting quarkonium boundstates in vacuum, we predicted the
masses for $1S$, $2S$, and $3S$ states of fully-heavy baryons. We also computed
the temperature dependence of baryon masses and the thermal widths in a hot QCD
medium. These properties are important to precise study of fully-heavy baryon
production in heavy ion collisions.
