  With the adiabatic assumption in the cooling process, we discussed a new
mechanism on Upsilon(1S) suppression that is due to the fast heating process at
the early stage of the fireball instead of its finite decay width in finite
temperature medium produced in the heavy ion collisions. We calculated the
transition probability after the fast heating dissociation as a function of the
temperature of the medium and the nuclear modification factor in central
collisions, and found that the suppression is not negligible at RHIC, even if
the width of Upsilon(1S) vanishes.
