Overheating in dwellings is a global concern that is increasing due to global warming and more frequent and extreme heatwaves. This study assesses the relationship between different building parameters (built period, floor level, orientation, window area and solar shading) and compares indoor overheating hours during summer in twelve apartments monitored in Pamplona (North of Spain). They were selected as samples from different Spanish built periods related to different energy regulations, without mechanical cooling and with some kind of exterior solar shading. Overheating hours were calculated using the UNE-EN 16798 standard, which establishes a maximum acceptable operative temperature. This limit is adaptive and it is defined as the exponentially weighted running mean of the daily outdoor temperature. Multilevel mixed-effects linear and logistic regressions were used to analyse and compare overheating hours. Floor level, window area and solar shading were the parameters that showed a significant relationship with indoor overheating hours (p < 0.01). Orientation and built period did not reach a statistically significant value (p > 0.01). It is particularly noteworthy that the apartments built under the current Spanish Energy Regulations (after 2006) do not show a significant reduction in indoor overheating hours compared to those built without any energy regulations. This assessment reveals that current building energy regulations may not be enough to avoid overheating or ensure adaptation to warmer conditions. Therefore, this study contributes to establishing the main building parameters to improve in order to adapt Spanish apartment buildings to warming conditions in temperate climates.