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In this work, a thermomechanically coupled rolling problem with nonlocal contact, Coulomb’s friction and heat exchange boundary conditions, for incompressible rigid-plastic, temperature-, equivalent strain- and strain-rate-dependent materials, is considered. A coupled variational formulation, consisting of a nonlinear variational inequality for the velocity, a nonlinear variational equation for the temperature and an evolution equation for the equivalent strain, is derived. A variable stiffness parameters method is proposed, its convergence is proved and existence and uniqueness results are obtained. [ABSTRACT FROM AUTHOR]