We study the folding of RNA secondary structures with quenched sequence randomness by means of the constrained annealing method. A thermodynamic phase transition is induced by including the conformational weight of loop structures. In addition to the expected melting at high temperature, a cold melting transition appears. Our results suggest that the cold denaturation of RNA found experimentally is, in fact, a continuous phase transition triggered by quenched sequence disorder. We calculate both hot and cold melting critical temperatures for the competing energy scenario between favorable and unfavorable base pairs and present a phase diagram as a function of the loop exponent and temperature.