I don't think it is possible without a lot of difficult and expensive changes. The CCC works on a completely different wiring and control system from any conventional thermostat.
One thing you can do though, is to wire a programable thermostat into the control wire going to the furnace. If you splice the programmable thermostat into one of the two wires going to the furnace, and then set the CCC for a highish temperature, the programmable will take command and run the furnace as long as the temperature is below what you set on the CCC. How easy this is to do will depend on the layout of your model, on ours it is fairly easy because the furnace is just under the kitchen counter where it is easy to get at the wiring. Of course, this only allows for programmable control of the heat, but that is all most people need.
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