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In order to improve the printing quality, this study focused on the thermo-fluid-solid coupling process of ink roller-ink. One of the highlights of this study is to consider the influence of temperature on the rubber hyperelastic parameters, viscoelastic parameters, and ink viscosity. The other highlight is to improve the elastohydrodynamic lubrication theory and Hertz contact theory through the rubber elastic modulus, which is determined by the relaxation curve considering the temperature and working conditions. Furthermore, based on the improved theory, the thermo-fluid-solid coupling model of ink roller-ink was established. Finally, the effect of temperature on the coupling process was analyzed. The results show that under the working conditions, with increasing temperature from 20 °C to 40 °C, the contact half-width increases from 4.2335 mm to 4.4701 mm, and the minimum ink film thickness decreases from 0.5097 mm to 0.1410 mm, and the maximum ink pressure decreases from 0.6802 MPa to 0.6618 MPa. [ABSTRACT FROM AUTHOR]