Additive Manufacturing (AM) offers transformative opportunities to create functionally hybridized, insulating, monolithic AM wall elements. The novel fabrication methods of AM allow for the production of highly differentiated building components with intricate internal and external geometries, aiming for reduced material use while integrating and enhancing building performance features including thermal insulation performance. This study focuses on integrating such thermal insulation performance by leveraging the individual features of three distinct AM processes: Selective Paste Intrusion (SPI), Selective Cement Activation (SCA), and Extrusion 3D Concrete Printing (E3DCP). Using a simulation-based parametric design approach, this research investigates 4,500 variations of monolithic AM façade elements derived from a generative hexagonal cell layout with differing wall widths, the three respective AM processes, different material compositions with and without lightweight aggregates, and three different insulation strategies, namely, air-filled cells, encapsulated lightweight aggregates, and additional insulation material within the cavities. Thermal performance feedback is realized via 2D heat flux simulations embedded into a parametric design workflow, and structural performance is considered in a simplified way via geometric and material-specific evaluation. The overall research goal is a multi-objective design optimization, particularly identifying façade configurations that achieve a U-value of less than 0.28 W/m2K and a theoretical compressive strength exceeding 2.70 MN per meter wall length. The results of this study detect 7% of all generated variations in line with these thermal and structural requirements, validating the feasibility of monolithic, thermally insulating AM wall elements. The presented workflow contributes to exploiting the potential of a new design of functionally hybridized AM components.