  We study time evolution of the $Q$ ball in thermal logarithmic potential
using lattice simulations. As the temperature decreases due to the cosmic
expansion, the thermal logarithmic term in the potential is eventually overcome
by a mass term, and we confirm that the $Q$ ball transforms from the thick-wall
type to the thin-wall type for a positive coefficient of radiative corrections
to the mass term, as recently suggested. Moreover, we find that the $Q$ ball
finally "melts down" when the $Q$-ball solution disappears. We also discuss the
effects of this phenomenon on the detectability of gravitational waves from the
$Q$-ball formation.
