This work describes the development and implementation of a large-deformation solver with thermomechanical friction contact for numerical simulation in applications such as friction welding processes. A finite strain associative coupled thermoplasticity model is used: this resolves the viscoplastic deformations in the thermomechanically affected zone as well as the elastic stresses in the parent material. An arbitrary Lagrangian–Eulerian (ALE) formulation for coupled finite strain thermoplasticity is developed and incorporated into the solver, in which the motion of the reference configuration is represented incrementally through a reference velocity field. Thus, the deformation from the material configuration is required neither explicitly in terms of a deformation field, nor implicitly in terms of the deformation gradient. While the finite element formulation and the solver are derived for the general 3D setting, the axisymetric approximation is made for application to a range of benchmark problems. These serve to elucidate features of the model and computational procedure, also through comparison with a fully Lagrangian approach. Simulation of a direct drive friction welding problem illustrates the robustness and reliability of the new numerical approach.