> In my house, our nursery both cooled faster and heated faster than any other room in the house. The thermostat (a Nest) controlled the boiler from the living area, and would often turn off the boiler while the nursery was still chilly.

This Home Assistant project is great fun, and I highly recommend playing with HASS to anyone who likes to play around with and maintain these things.

But for anyone looking for an easier solution: Ditch the Nest and get an ecobee with remote sensors. Nest has remote sensors as well, but you can only pick one. ecobee will average across the sensors you choose. It also has a mode that can follow occupancy detection and prioritize rooms with movement, but that's not useful for a nursery with a sleeping baby like this.