[indigomm]

Modern thermostats are a bit better than simply turning the boiler on when cold, off when hot. They are Time Proportional & Integral (TPI) devices. Put simply, they 'learn' the characteristics of the room - how long it takes to heat up and how much heat it needs to maintain the temperature. This is then used to work out how much to cycle the boiler on/off to keep the actual temperature much closer to the set point. Less variation makes for a much more comfortable room with less temperature swing than a simple thermostat can do. I see no reason this couldn't be built into HASS, but to my knowledge it isn't in there.

Also, modern boilers have digital control such as OpenTherm. They aren't just simple on/off devices, but instead vary their output based on the heat demand. The heating controller works out the temperature losses across the system, and gets the boiler to moderate the flow to match. This means that instead of turning on and off all the time, the boiler runs continuously at a low rate. More efficient with less wear and much tighter temperature control.

[dtgriscom]

Even mechanical thermostats have heat anticipator settings. When the thermostat turns the furnace on, it also turns on a small heater in the thermostat. This simulates the heat that will continue to arrive (thermal momentum, as it were) after the furnace is turned off. Otherwise, the temperature will forever be overshooting the thermostat setting.

https://inspectapedia.com/heat/Heat_Anticipator_Adustment.ph...

[lima]

Danfoss Ally thermostats have a built-in PID controller that does this, and can be used with Home Assistant via zigbee2mqtt.

In theory, you could use aggregate heat demand from the Ally thermostats to control a modulating OpenTherm boiler.