  We consider the 1D motion of an overdamped Brownian particle in a general
potential in the low temperature limit. We derive an explicit expression for
the probability distribution for the heat transferred to the particle. We find
that the local minima in the potential yield divergent side bands in the heat
distribution in addition to the divergent central peak. The position of the
bands are determined by the potential gaps. We, moreover, determine the tails
of the heat distribution.
