In this work, we report the development and experimental validation of a coupled statistical thermodynamic model allowing prediction of the structural transitions executed by a novel DNA nanodevice, for quantitative operational design. The efficiency of target structure formation by this nanodevice, implemented with a bistable DNA molecule designed to transform between three distinct structures, is modeled by coupling the isolated equilibrium models for the individual structures. A peculiar behavior is predicted for this nanodevice, which forms the target structure within a limited temperature range by sensing thermal variations. The predicted thermal response is then validated via fluorescence measurements to quantitatively assess whether the nanodevice performs as designed. Agreement between predictions and experiment was substantial, with a 0.95 correlation for overall curve shape over a wide temperature range, from 30 C to 90 C. The obtained accuracy, which is comparable to that of conventional melting behavior prediction for DNA duplexes in isolation, ensures the applicability of the coupled model for illustrating general DNA reaction systems involving competitive duplex formation. Finally, tuning of the nanodevice using the current model towards design of a thermal band pass filter to control chemical circuits, as a novel function of DNA nanodevices is proposed.