  We determine the probability that a partially melted heteropolymer at the
melting temperature will either melt completely or return to a helix state.
This system is equivalent to the splitting probability for a diffusing particle
on a finite interval that moves according to the Sinai model. When the initial
fraction of melted polymer is f, the melting probability fluctuates between
different realizations of monomer sequences on the polymer. For a fixed value
of f, the melting probability distribution changes from unimodal to a bimodal
as the strength of the disorder is increased.
