A method is developed for the calculation of the ground-state melting curves ( o vs.T) for random, infinite heteropolymers. Here o is the ground-state value of the fraction of melted links ( o in the strong cooperativity approximation). It is shown that the differential melting curves (d /d T vs.T) can have a fine structure in the form of several peaks on the bell-shaped main curve. Positions, magnitudes, and widths of these peaks are estimated. The accidental fine structure of melting curves, which is caused by a finite length of the polymer, is briefly discussed.