Cities on the east Mediterranean coast, especially in Palestine, are struggling to move towards sustainability as they are vulnerable to climate change and lack natural resources, especially energy resources, and this situation is further aggravated by high energy prices. The problem is the building sector, which is the most challenging sector when it comes to cities’ sustainability and, specifically, energy sustainability. In Palestine, this sector is the main consumer of energy but it lacks energy efficiency measures, such as up-to-date building energy codes. This study analyzed building thermal performance under different scenarios with a focus on building envelopes. We aimed to evaluate the benefits of introducing an updated building energy code—mainly addressing U-values for building envelopes—on future reductions in energy demand. We used a simulation tool (DesignBuilder) to evaluate typical existing building-envelope thermal and energy performances. Then, we undertook a comparison between the existing conditions and the proposed application of different scenarios, including the existing Palestinian building energy code and green building guidelines, the ASHRAE code for building envelopes, and the Jordanian building energy code, in order to introduce an updated building envelope energy code. The results showed that the current situation—building without applying any energy code or applying the existing Palestinian building energy code—is far from the high-energy performance that could be achieved by applying international or local green building codes. The use of thermal insulation could reduce the energy demand for heating by 83 to 43%, depending on the building type, climatic zone, and U-value. We recommend utilizing different U-values for building envelopes in different climatic zones to achieve high thermal performance. The results from this study have implications for construction industry professionals, local governments, and researchers seeking to establish high-energy-performance building envelopes.