There are more frequent and intense heatwaves in Europe due to climate change. Due to these rare meteorological sequences, the building envelope often fails to provide adequate protection. As we spent most of our time inside buildings, it is necessary to assess the thermal performance of the building during extreme meteorological sequences. Our focus is on determining the principal harmonics of the external temperature that are not damped by the building’s envelope during summer time. Therefore, we have developed a methodology to represent the external temperature, which is divide in two zones, a thermal load zone, and a thermal overload zone. The construction of this theoretical external temperature is parametrized using the modal method and the Discrete Cosine Transform. Finally, the methodology is applied to a case study in Paris focusing on the well-known heatwaves, leading to the ...