In this paper, we study simultaneous distributed-boundary optimal control problems on the internal energy and the heat flux for a system governed by a class of elliptic boundary hemivariational inequalities with a parameter. The system has been originated by a steady-state heat conduction problem with non-monotone multivalued subdifferential boundary condition on a portion of the boundary of the domain described by the Clarke generalized gradient of a locally Lipschitz function. We prove existence and asymptotic behavior results for the optimal controls and the system states for the optimal control problems, when the parameter, like a heat transfer coefficient, tends to infinity on a portion of the boundary.