Active building envelopes that act as energy converters—gathering on-site available renewable energy and converting it to thermal energy or electricity—is a promising technological design niche to reduce energy consumption in the building sector, cut greenhouse gas emissions, and thus tackle climate change challenges. This research adds scientific knowledge in the field of composite building envelope structures containing phase-change materials for thermal energy storage. In this study, the focus lies on the cooling phase of the diurnal gain and release of solar energy. The experimental setup imitates day and night environment. Six alterations of small-scale solar facade modules are tested in two different configurations—with and without the adjustable insulation layer on their outer surface during the discharging phase. Modules explore combinations of aerogel, air gap, and Fresnel lenses for solar energy concentration. The results allow us to compare the impact of the application of an additional insulation layer at “night” for different designs of solar facade modules. The results show that modules with an air gap provide higher heat gains but do not take full advantage of the latent heat capacity of phase-change materials.