<p>This paper presents a novel mathematical analysis of a quasistatic frictional contact problem involving thermo-viscoelastic materials interacting with a thermally conductive foundation. The contact is governed by unilateral constraints, and friction is modeled using Coulomb’s law. We derive a variational formulation leading to a coupled system describing displacement and temperature fields. Our main contributions include establishing the existence and uniqueness of weak solutions under general assumptions, analyzing the sensitivity of solutions to perturbations in the contact boundary conditions, and formulating and studying an associated optimal control problem, for which we prove the existence and convergence of optimal solutions. These results provide a rigorous theoretical foundation for the design and control of engineering systems involving frictional contact and thermal effects, with potential applications in material design, mechanical systems, and thermal management.</p>