It is well known that under certain circumstances a mixture of coarse, hot (molten) drops in water that forms from pouring a hot melt into water explodes. This so-called "steam explosion" is generally believed to involve fine fragmentation of the melt drops induced by steam bubble collapse and concomitant water vaporization on a timescale that is short compared with the steam pressure relief time. Motivated by a previously published idea that rapid solidification would render uranium oxide (UO2)-containing (corium) melt drops stiff and resistant to the fragmentation induced by steam bubble collapse that is requisite for an explosion, here we combine solidification theory with an available theory of the stability of thin, submerged crusts subject to acceleration to predict the "cutoff time" beyond which melt drop fragmentation is suppressed by crust cover rigidity. Illustrative calculations show that the cutoff time for corium melt drops in water is a fraction of a second and probably shorter than the time it takes to form the coarse-premixture configuration of melt drops in water that is a prerequisite for an explosion, while the opposite is true for the molten aluminum oxide (Al2O3)-water system for which the window of opportunity for an explosion is predicted to be several seconds. These theoretical findings are consistent with previous experiments that revealed molten UO2 or corium pours into water to be nonexplosive and produced steam explosions upon pouring molten Al2O3 into water.