  We use the non-perturbative Q\bar Q potential at finite temperatures derived
in the Field Correlator Method to obtain binding energies for the lowest
eigenstates in the Q\bar Q and QQQ systems (Q=c,b). The three--quark problem is
solved by the hyperspherical method. The solution provides an estimate of the
melting temperature and the radii for the different diquark and triquark bound
states. In particular we find that J/\psi and $ccc$ ground states survive up to
T \sim 1.3 T_c, where T_c is the critical temperature, while the corresponding
bottomonium states survive even up to higher temperature, T \sim 2.2 T_c.
