Many biological process and function centers around recognition of double stranded RNA as it impacts numerous pathways associated with maturation of cellular RNA. This work assembles an intricate thermodynamic profiling of the phenothaizinium dyes methylene blue and new methylene blue with three double stranded ribonucleic acids, poly(A).poly(U), poly(C).poly(G) and poly(I).poly(C) with aid of thermal helix melting, isothermal titration calorimetry and differential scanning calorimetry experiments. Isothermal titration calorimetry had put forward that highest binding affinity was observed for poly(A).poly(U)-dye binding while the order varied as poly(A).poly(U) > poly(C).poly(G) > poly(I).poly(C). Strong stability of the polynucleotides against heat strand separation characterises the binding. Non-electrostatic component had larger share in parsing of the standard molar Gibbs energy of the binding. The processes' negative change in heat capacity is evidence of how essential hydrophobic forces are. Release of water molecules which are in random orientation mode occurs from RNA's hydrophobic binding pockets. Negative enthalpy and positive entropic change are the two significant features in this hydrophobic binding scenario. Another vital result of enthalpy-entropy compensation has been identified with the binding processes. The findings bear direct and ubiquitous acknowledgement in revitalizing our interest and broadening our horizon towards successful targeting of small molecules to RNAs.