Cut off power to the furnace using the emergency shutoff or breaker switch, then unscrew the thermostat's mounting bracket. As you disconnect each wire from its terminal, label the wire with the letter of the terminal it came from. Tape the wires to the wall so that you don't lose them. Some older thermostats contain mercury; for information on proper disposal, go to the Thermostat Recycling Corporation.
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Drill/driver, for mounting the outdoor sensor