Nowadays, a large amount of the total primary energy is consumed by buildings, accounting for about 40% of the total energy demand. Aligned with the EU objectives and the strategies to reduce the demand, cooling and heating are stated as the most energy consuming processes and the building envelope plays an important role to reduce the energy consumption. In this work, the energy demand related to heating and cooling in a typical building has been evaluated, which has been simulated in 35 cities located in different climatic zones, using the DesignBuilder v.6.1.7.007 software. Although the increase in insulation and the replacement of windows lead to a reduction in energy demand, in the case of the cities of Santa Cruz de Tenerife and Las Palmas de Gran Canaria without insulation, the demands are lower than 1.7 kWh/m2/year and 5 kWh/m2/year, respectively, and these results indicate that energy saving strategies, driven by policies and economic support, based on the renovation and improvement of the thermal insulation of the building envelope, are not the most appropriate due to the need for an additional energy load for cooling and to maintain comfort within the regulatory limits.