Do smart thermostats work without internet connection?

I want buy a smart thermostat but obviously don’t want it connected to the internet. I have a remote access server that I use to access my network already. I have security cameras blocked by my firewall but I can still access remotely. Will this work with smart thermostats? I can’t find anything on Brave about this. I heard smart thermostats don’t work if they can’t phone home. Also what about other IoT things like lights? Thanks

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