Spectrophotometry has been used to investigate the interaction of methyl orange (MO), an azo dye as a guest, with β-cyclodextrin (CD) as the host. Inclusion of methyl orange into β-cyclodextrin nanocavity leads to two orientational isomers, so-called inclumers, because of the asymmetric structure of methyl orange. This study was performed in basic and acidic media to yield the microconstants and thermodynamic parameters for inclusion complex formation equilibria in each media. The recorded data set at a constant temperature is rank deficient, because there is a linear dependency between concentration profiles of inclumers. This problem is overcome through the augmentation of multiwavelength data recorded at different temperatures. Titration of methyl orange solution with β-cyclodextrin solution was performed in five different temperatures, in order to calculate the formation microconstants for inclumers, pure spectra for absorbing components in each media and thermodynamic parameters such as change in enthalpy, entropy and Gibbs free energy for inclusion equilibria. Then globalization was performed to analyze the augmented data sets. The titration of acidic methyl orange with sodium hydroxide was also performed, to calculate the microconstants and thermodynamic parameters related to ionization. The interaction of the basic form of methyl orange with β-cyclodextrin in basic medium led to two orientational isomers. In acidic medium methyl orange has two tautomeric forms, called ammonium and azonium. The inclusion of azonium in β-cyclodextrin has been neglected in the considered model for simplicity and the inclusion of ammonium is modeled, because it forms more stable complexes with β-cyclodextrin nanocavity. Newton–Raphson algorithm was used to produce concentration profiles and Newton–Gauss–Levenberg/Marquardt algorithm was used to optimize the parameters of interest.