With increasing desire for a carbon-neutral building sector, both pre- and post-World War II (WWII) buildings pose a significant retrofitting potential but also several challenges. Internal insulation is often the only viable solution for preserving the exterior aesthetics of historic buildings however, it can exacerbate moisture-related risks such as interstitial condensation, mould growth, and material decay. Post-WWII buildings, commonly constructed with concrete, aerated concrete, and cavity wall systems, are also energy inefficient compared with today’s standards and contribute substantially to the built environment’s carbon footprint. Despite this, little research exists on the hygrothermal performance of these modern/industrial era façades, particularly under future climate conditions characterized by increased outdoor humidity and precipitation. This study addresses this gap by investigating the hygrothermal behavior of 10 typical Danish heavy-weight wall constructions—two pre-WWII solid masonry walls and eight post-WWII constructions—when retrofitted with internal insulation. The study evaluates performance under projected climate conditions 2020–2050 to assess moisture risks and insulation feasibility for two different type systems. Simulation results show critical relative humidity levels and indicate potential mould growth risk in the wall/insulation interface in most of the solid façade constructions. For cavity façade constructions, while certain types showed medium-high relative humidity, the mould risk was generally low in these walls. Future climate simulations mostly show increasing relative humidity and mould risk, with some exceptions. In addition, comparison between the two examined insulation systems indicate that the diffusion-tight mineral wool system was more sensitive to the changing climate conditions than the highly diffusion-open insulation system.