Replacing a three-wire Cadet thermostat with a two-wire thermostat can be done. To ensure the proper function of your heating and cooling system, you should install a three-wire thermostat as soon as possible. A two-wire thermostat can only control either the cooling system or the heating system; it cannot control both. Only a three-wire thermostat can control both. So, when you use a two-wire system, you will only get access to either cooling or heating. If it's an emergency, the two-wire thermostat can provide you with cooling or heating.
Turn off the power to the thermostat in the circuit breaker. If your circuit breaker is not marked, just turn off the main circuit breaker to turn off power to the whole hose, to be safe.
Remove the old thermostat, using the screwdriver to pry open the top. Remove any screws that hold in place the thermostat with the screwdriver. Remove all wires connected to the old thermostat.
Twist the green ground cables together, then screw on a wire nut. The cables will be inside the electrical cable box that the thermostat was connected to.
Twist the white neutral wires together and screw on a wire nut inside the electrical box.
Connect one of the black cables from the thermostat to one of the black cables in the electrical box. Twist the cables together, and screw on a wire nut.
Connect the remaining black wire from the thermostat to the remaining black wire in the electrical box, twist them together and screw a wire nut on the end of the wires.
Tape the remaining two red wires separately with electrical tape on the tip, so it does not cause a short. Push the thermostat into place. Read the manual for specific directions on placing the thermostat on the wall as it varies by model.
Turn back on the circuit breaker and test the thermostat. If the thermostat does not work, check for loose wires. Either the cooling system or the heating system will work. Once you've verified which system is working and which one is not, you can rewire the thermostat to change which one is active. To switch which system is active, replace the black wires with the red wires and tape the ends of the black wires instead.