If it's actually using radio, almost certainly there is a radio receiver unit at your furnace which converts the radio commands to simple voltages on physical

If it's actually using radio, almost certainly there is a radio receiver unit at your furnace which converts the radio commands to simple voltages on physical wires, likely to power a 24v solenoid. All you need to do is hook in a esp32 or similar to also send those voltages when it receives a command.