Recently we have found that Chelerythrine, a benzophenanthridine alkaloid induce self structure formation in polyriboadenylic acid but the binding is non-cooperative.
Non-cooperative transition is rather attributed to the curve with series of steps (each step reflects melting of a region with different stability). In my opinion self-complementary or intramolecular folding can give cooperative or non-cooperative folding - all depends on sequence and disturbance/"homogeneity" of the secondary structure that you work with.
Besides, according to literature, polynucleotides (also polyA) undergo helix-coil transition, but a single helix is rather formed (stabilised by stacking interactions). At low temperature a helical rod-like structure is formed, and melted to random coil after increasing the temperature. It results in a broad melting curves and non-cooperative transitions.