According to the EU Directive on the energy performance of buildings, by 2030 all new buildings must be zero-emission buildings, and by 2050 the existing building stock should be entirely decarbonized. The goal is partly to be achieved through electrification, with heat pumps playing a significant role in this shift. Meanwhile, the refrigerants used by most heat pumps today are characterized by high carbon footprints, which is the reason for their gradual replacement with environmentally neutral ones. However, this replacement is often associated with a trade-off—diminished seasonal and annual performance of the respective heating and cooling systems. This study investigates the possibility of utilizing passive building envelope elements—in the presented case, the provision of fixed external shading—as an accompanying measure to reduce the energy demands and to facilitate the replacement of a typical present-day HVAC system, employing a refrigerant with high global warming potential, with a natural refrigerant-based alternative. The analysis involves dynamic simulations with TRNSYS and is based on a case study of an existing lecture hall with substantial solar heat gains.