This article demonstrates a large-scale 3D topology optimization problem formulation for components in need of internal cooling owing to surrounding hot gas flow. A conjugate heat transfer model is used and the goal of the optimization problem is to maximize the thermal performance subject to a coolant consumption limit. As a model problem, the interior design of a gas turbine guide-vane-like geometry is considered. High-quality finite element meshes are generated automatically by means of a voxelization method. A structural compliance constraint for thermo-mechanical loads, and a constraint for the suppression of free-floating structural parts, are included in the problem formulation. For the latter, an analytical expression for the constraint limit is derived. Several numerical examples indicate that the proposed problem formulation is able to generate interesting conceptual designs for interior-vane-cooling solutions.