European Building Codes have transitioned towards Net Zero Energy Building (NZEB) requirements in new constructions, demanding high levels of insulation and airtightness derived from research and standards developed in Northern and Central Europe. The use of these principles in Southern Europe, where solar radiation is greater and building typologies and user behaviour are different, may have had a negative impact in Thermal Comfort and Energy Demand and Consumption. In this study, six dwellings located in a 2018 27-storey Passivhaus-certified building were monitored for a period of 9–18 months in 2019 and 2020. In the spirit of a complete Post-Occupancy Evaluation, a User Comfort Survey was carried out. The obtained data were analysed and fixed-limit and adaptative comfort models were used to assess the compliance of several European Comfort Standards, namely, EN ISO 7730, EN 15251, CIBSE TM:52, CIBSE TM:59 and CIBSE Guide A. Experimental results confirmed the issues reported by occupants in the Comfort Survey, making evident a severe overheating problem which we were able to quantify. In addition to presenting the obtained data and its analysis, this paper discusses the plausible causes and health-related implications of excess heat in NZEB Housing in the Northern Spanish climate.