Switching component in Nest Thermostat?
Use google to search for "Nest thermostat teardown". Many teardowns show there are no relays inside so it might not even use "switching" (like most traditional thermostats do), the Nest can use a protocol like OpenTherm.

Protocols like OpenTherm allow finer control of the heating system. Instead of just on/off there will also be commands like "20% of full capacity" to prevent "overshoot" and making the heating more efficient.

For a DIY thermostat however it is much easier to use the traditional on/off switching. Usually this is done using a relay. Even more convenient is a latching relay, which only needs to be energized (and use power) when it switches on or off. That way it is possible to make a thermostat that runs on batteries. A non latching relay would quickly drain the batteries as it needs to be energized all the time when it needs to be on.

It should be very well possible to use some solid-state switch instead of the relay like a MOSFET which also does not require power to be kept on.