We model the spectral changes of late oxygen-rich Miras observed in different pulsation phases. From a combination of variable near-IR spectra and UKIRT spectro-photometry of the 9.7-μm silicate dust emission feature in different phases we study the influence of the changing atmospheric circumstances on the conditions in the circumstellar dust shell. From a detailed modelling of TiO and VO bands in the near-IR spectra, we determine changes of the effective temperature and the effective atmospheric acceleration of the central star. The corresponding model spectral energy distribution is redistributed through the dust shell by means of radiative transfer calculations in order to perform a detailed modelling of shape changes observed in the silicate feature. We show that the latter are mainly caused by changes in the flux distribution of the incident radiation field with stellar pulsation, whereas intensity changes of the dust emission result from stellar luminosity changes as they are enshrouded by very optically thin dust shells. In the case of the Mira o Cet we compute that the effective temperature increases from Teff=2400 K in the minimum phase to 3000 K (±100 K) around the maximum phase. The amplified momentum transfer around maximum light enhances the acceleration of the dust outflow near the dust condensation radius of ∼6 R∗. This produces variations of the terminal dust outflow velocity with phase (Δv∞≃5 km s−1) at larger distance from the star. The corresponding small changes in flux mean opacity and gas mass-loss rates (from 2.8 to 3.2×10−7 M⊙ yr−1) are sufficient to model the shape changes observed in the dust emission feature. A comparison with the modelling results for another long period Mira, U Ori, is also provided.