In this paper we propose multispectrum rotational states distribution thermometry as an optical method for primary thermometry. It relies on a global fitting of multiple absorption lines of the same band at different pressures. The approach allows leveraging both the temperature-dependent Doppler width and the temperature-dependent distribution of line intensities across the ro-vibrational band. We provide a proof-of-principle demonstration of the approach on the 3ν 1 + ν 3 band of CO2, for which several accurate line-strength models of both theoretical and experimental origin are available for the global fitting. Our experimental conditions do not allow to test the methodology beyond a combined uncertainty of 530 ppm, but the comparative analysis between different line-strength models shows promise to reduce the error budget to few tens of ppm. As compared to Doppler-broadening thermometry, the approach is advantageous to mitigate systematic errors induced by a wrong modelling of absorption line-shapes and to reduce, for a given experimental dataset, the statistical uncertainty by a factor of 2. When applied in a reverse way, i.e. using a gas of known temperature, the approach becomes a stringent testbed for the accuracy of the adopted line-strength model.