  In a previous paper (cond-mat/0106554) we showed the existence of two new
zero-temperature exponents (\lambda and \theta') in two dimensional Gaussian
spin glasses. Here we introduce a novel low-temperature expansion for spin
glasses expressed in terms of the gap probability distributions for successive
energy levels. After presenting the numerical evidence in favor of a
random-energy levels scenario, we analyze the main consequences on the
low-temperature equilibrium behavior. We find that the specific heat is
anomalous at low-temperatures c ~ T**\alpha with \alpha=-d/\theta' which turns
out to be linear for the case \theta'=-d.
