properly programmed they should be able to cut heating and cooling bills (and joules) significantly
PID is a regulator. If you want anything more complex than a constant reference signal for it to regulate to, you're talking a supervisory controller with a programmed feedforward signal. Once you have that, trivial extension to further optimize based on weather reports etc.
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Sure that would be a good obvious design, Fall back to basic paid regulation to 65 drug or whatever if WiFi fails. No either-or here.
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