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.
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