<p>This paper investigates an optimal control problem governed by a system of mixed hemivariational–variational inequalities arising in the modeling of Bingham-type fluid flows with thermal effects. The model incorporates non-smooth and non-monotone slip boundary conditions, as well as nonlinear thermal coupling. The boundary conditions for both velocity and temperature involve the generalized Clarke subdifferential. The associated weak formulation leads to a coupled system of mixed hemivariational–variational inequalities. We establish the existence and uniqueness of solutions and analyze their continuous dependence on the data. Additionally, we prove the existence of optimal controls.</p>