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Organic molecules have recently gained attention as novel sources of single photons. We present a joint experiment--theory analysis of the temperature-dependent emission spectra, zero-phonon linewidth, and second-order correlation function of light emitted from a single molecule. We observe spectra with a zero-phonon-line together with several additional sharp peaks, broad phonon sidebands, and a strongly temperature dependent homogeneous broadening. Our model includes both localised vibrational modes of the molecule and a thermal phonon bath, which we include non-perturbatively, and is able capture all observed features. For resonant driving we measure Rabi oscillations that become increasingly damped with temperature, which our model naturally reproduces. Our results constitute an essential characterisation of the photon coherence of these promising molecules, paving the way towards their use in future quantum information applications.