A general method for estimating the statistical barrier height distribution in a disordered system is presented. The method is based on the interpretation of the temperature dependence of the instantaneous normal mode density of states. An integral equation is derived which relates the fraction of unstable instantaneous normal modes at a particular temperature to the intrinsic distribution of one-dimensional energy barriers g(E) for the 3N - 6 internal degrees of freedom in the system. We argue that the overall distribution of multidimensional barriers on the potential energy hypersurface Gamma(E) is a Gaussian distribution with a mean and variance which can be calculated from the intrinsic barrier height distribution g(E). A technique for solving the integral equation is presented and applied to derive the energy barrier distribution for the isobutyrl-val-ala(2)-methylamide tetrapeptide, the S-peptide of ribonuclease A, and the bovine pancreatic trypsin inhibitor. We compare our results with the random energy model and suggest how parameters for the statistical Hamiltonian used in that theory might be derived using computer simulation.