Tire production is a complex process due to large deformations, highly non-linear uncured rubber material and large temperature. It can be observed, that the production conditions have a strong influence on the cured tire behaviour and should be studied to minimize possible defects in the final product. In this contribution, an Arbitrary Lagrangian Eulerian (ALE) formulation is presented to overcome convergence issues stemming from large distortion of elements in a pure Lagrangian description. In an ALE formulation, the computational mesh is not fixed in space and can move relatively to the material motion, which allows to control the distortion of the mesh by a smoothing algorithm. Coupling the material motion with the newly obtained mesh is done by an advection algorithm to project the internal variables of a thermo-mechanically consistent material model. Based on the assumption that the internal variables are projected directly from the integration points, an additional mesh is generated with the integration points of the old mesh as grid. To show the capabilities of the presented algorithm, several numerical examples are shown ranging from a simple forging example to a complex tire production process.