A theoretical and computational framework for the analysis of fully transient, thermomechanically coupled, frictional rolling contact based on an arbitrary Lagrangian–Eulerian (ALE) kinematical description is presented. In particular, a computationally efficient methodology for mixed control between the ALE referential velocities and their corresponding driving forces is developed and discussed in depth. Numerical examples involving two-dimensional (2D) cylinder–plate rolling contact are presented, covering a range of transient, thermomechanically coupled rolling contact phenomena, taking place on a broad range of time scales. Here, particular points of emphasis include dynamical effects in the vicinity of the contact region and the time scales on which mechanical and thermal mechanisms operate.

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