[kenhwang]

The connection between the furnace and the thermostat probably shouldn't go through the internet.

So it's perfectly reasonable for the furnace to turn off when it is disconnected, because disconnection would be a very strong signal for an error state instead of regular intermittent network/service issues.

[duped]

They're not, "smart" thermostats have a WiFi frontend that allows devices to connect to it from the network but the thermostat itself is hardwired to the furnace/HVAC.

You could in theory put one next to the furnace in your machine closet but that would be dumb and expensive

[InitialBP]

I have a nest and it's wired directly to your furnace via the thermostat control wires.

While it is controllable via the cloud, even without wifi it continues to function.

[kgermino]

Are there any furnaces that do that?

Certainly, the standard smart thermostat set up is that your ecobee is connected to the Internet, but controls the furnace using good old-fashioned signal wires

[sokoloff]

Which is only extremely tangentially related to "if I pull my thermostat off the wall"

The overwhelmingly most common connection between a thermostat and furnace is a contact closure when calling for heat, with no ability to differentiate between “thermostat is present but not calling for heat” and “thermostat is not present” as both present as "these T-T contacts are not closed/shorted together".

[baq]

the connection to my thermostat is via a cable, if I pull it out of the wall it won't be connected to anything at all. the whole furnace is not connected to anything but mains power.