Rolling resistance dictates a large part of the energy consumption of trucks. Therefore, it is necessary to have a sound understanding of the parameters affecting rolling resistance. This article proposes a semi-physical thermodynamic tyre rolling resistance model, which captures the essential properties of rolling resistance, such as transient changes due to temperature effects and the strain-amplitude dependency of the viscous properties. In addition, the model includes cooling effects from the surroundings. Both tyre temperature and rolling resistance are obtained simultaneously in the simulation model for each time step. The nonlinear viscoelasticity in rubber is modelled using the Bergström–Boyce model, where the viscous creep function is scaled with temperature changes. The cooling of the tyre is considered with both convective and radiative cooling. Moreover, the article explains different material parameters and their physical meaning. Additionally, examples of how the model could be used in parameter studies are presented.