Those who live in a pile of bricks from a previous century are aware that it takes some time to warm up on return from holiday.

This paper which studies the relationship between indoor and outdoor temperatures, using some physics informed statistics. The time period of the study is stated as being from 2-27 years but only 7 residences. One is left thinking about how different categories of building would behave if the study could be widened.
The take away message is that indoor temperatures rise and cool more slowly than outdoor ones with a delay of about 260 minutes (about 4 hours or so) and that the effects of a heatwave persist in the building for about 5 days after the heat wave has finished.
A few questions arise.