Façade elements are a building component that satisfies multiple performance parameters. Among other things, “advanced façades” take advantage of hybrid solutions, such as assembling laminated materials. In addition to the enhanced mechanical properties that are typical of optimally composed hybrid structural components, these systems are energy-efficient, durable, and offer lighting comfort and optimal thermal performance, an example of which is the structural solution developed in collaboration with the University of Zagreb and the University of Ljubljana within the Croatian Science Foundation VETROLIGNUM project. The design concept involves the mechanical interaction of timber and glass load-bearing members without sealing or bonding the glass-to-timber surfaces. Following earlier research efforts devoted to the structural analysis and optimization of thus-assembled hybrid Cross-Laminated Timber (CLT)-glass façade elements, in this paper, special focus is given to a thermal and energy performance investigation under ordinary operational conditions. A simplified numerical model representative of a full-size building is first presented by taking advantage of continuous ambient records from a Live-Lab mock-up facility in Zagreb. Afterwards, a more detailed Finite Element (FE) numerical analysis is carried out at the component level to further explore the potential of CLT–glass façade elements. The collected numerical results show that CLT–glass composite panels can offer stable and promising thermal performance for façades similar to national and European standard requirements.