When the heat wave struck, initially that thermal inertia works in your favour as the cool building keeps the interior cool. But after a day or two it heats up. Once that happens, the temperature at night doesn't drop. As you say, ventilation is not good, so the humidity rises too. The thing becomes an overnight sauna.
After one night of this, I went looking for a fan. In my Australian home, every room has a ceiling fan. In this German dwelling (rented by my daughter, an Aussie, for the past few years) there wasn't a single fan in the house, and worse none of the nearby shops sold fans. It looked to me like there was no "social knowledge" of fans or how to handle heat in general. I eventually got a fan off Amazon, who thankfully delivered the next day.
We were also there in another year in winter. These same buildings were amazing the cold. They could maintain a cosy inside temperature with very little extra energy. But geeze, you don't want to be in one in a heatwave that goes on for days.