The effect of sequence disorder on thermodynamics of ssRNA is investigated on the basis of constrained annealing approach. The random sequence with bimodal disorder is addressed. The temperature behavior of entropy, internal energy, specific heat and helicity degree is examined. Specifically, in presence of competing interactions model exhibits not only partial high-temperature denaturation, but also partial cold denaturation, when ssRNA melts with the system cool down. The comparison is carried out with the results obtained by McCaskill algorithm. It is shown that the constrained annealing approach gives a good agreement with the dynamic programming method.